Interesting Science fact #8
Copper is the only metal that is
naturally antibacterial.
PHYSICAL
SCIENCES
Content Booklet:
Targeted Support
GRADE 11 TERM 2
A MESSAGE FROM THE NECT
NATIONAL EDUCATION COLLABORATION TRUST (NECT)
Dear Teachers
This learning programme and training is provided by the National Education Collaboration Trust
(NECT) on behalf of the Department of Basic Education (DBE)! We hope that this programme
provides you with additional skills, methodologies and content knowledge that you can use to
teach your learners more effectively.
What is NECT?
In 2012 our government launched the National Development Plan (NDP) as a way to eliminate
poverty and reduce inequality by the year 2030. Improving education is an important goal in
the NDP which states that 90% of learners will pass Maths, Science and languages with at least
50% by 2030. This is a very ambitious goal for the DBE to achieve on its own, so the NECT was
established in 2015 to assist in improving education.
The NECT has successfully brought together groups of people interested in education so that
we can work collaboratively to improve education. These groups include the teacher unions,
businesses, religious groups, trusts, foundations and NGOs.
What are the learning programmes?
One of the programmes that the NECT implements on behalf of the DBE is the ‘District
Development Programme’. This programme works directly with district officials, principals,
teachers, parents and learners; you are all part of this programme!
The programme began in 2015 with a small group of schools called the Fresh Start Schools
(FSS). Curriculum learning programmes were developed for Maths, Science and Language
teachers in FSS who received training and support on their implementation. The FSS teachers
remain part of the programme, and we encourage them to mentor and share their experience with
other teachers.
The FSS helped the DBE trial the NECT learning programmes so that they could be improved
and used by many more teachers. NECT has already begun this scale-up process in its
Universalisation Programme and in its Provincialisation Programme.
Everyone using the learning programmes comes from one of these groups; but you are now
brought together in the spirit of collaboration that defines the manner in which the NECT works.
Teachers with more experience using the learning programmes will deepen their knowledge and
understanding, while some teachers will be experiencing the learning programmes for the first
time.
Let’s work together constructively in the spirit of collaboration so that we
can help South Africa eliminate poverty and improve education!
www.nect.org.za
CONTENTS
PROGRAMME ORIENTATION
PHYSICAL SCIENCES PLANNING AND PREPARATION
EXAM PREPARATION
USEFUL REVISION RESOURCES
4
10
15
16
INTRODUCTION
SEQUENTIAL TABLE
GLOSSARY OF TERMS
ASSESSMENT OF THIS TOPIC
BREAKDOWN OF TOPIC AND TARGETED SUPPORT OFFERED
TARGETED SUPPORT PER SUB TOPIC
17
18
19
20
21
22
INTRODUCTION
SEQUENTIAL TABLE
GLOSSARY OF TERMS
ASSESSMENT OF THIS TOPIC
BREAKDOWN OF TOPIC AND TARGETED SUPPORT OFFERED
TARGETED SUPPORT PER SUB TOPIC
39
40
41
42
43
44
INTRODUCTION
SEQUENTIAL TABLE
GLOSSARY OF TERMS
ASSESSMENT OF THIS TOPIC
BREAKDOWN OF TOPIC AND TARGETED SUPPORT OFFERED
TARGETED SUPPORT PER SUB TOPIC
52
53
54
55
56
57
INTRODUCTION
SEQUENTIAL TABLE
GLOSSARY OF TERMS
ASSESSMENT OF THIS TOPIC
BREAKDOWN OF TOPIC AND TARGETED SUPPORT OFFERED
TARGETED SUPPORT PER SUB TOPIC
74
75
76
77
78
79
TOPIC 5: GEOMETRICAL OPTICS
TOPIC 6: 2D AND 3D WAVEFRONTS
TOPIC 7: IDEAL GASES AND THERMAL PROPERTIES
TOPIC 8: QUANTITATIVE ASPECTS OF CHEMICAL CHANGE
17
39
52
74
PROGRAMME ORIENTATION
PROGRAMME ORIENTATION
Welcome to the NECT Physical Sciences learning programme! This CAPS compliant
programme consists of:
•
A Content Booklet: Targeted Support
•
Worksheet Booklet
•
A Planner & Tracker to help you plan lessons and monitor curriculum coverage
•
A Practical Booklet and Videos
•
A Set of Posters
•
A Formal Assessment Support Booklet
OVERVIEW AND APPROACH OF PROGRAMME
The FET Physical Sciences curriculum is long and complex. There are many quality textbooks
and teachers’ guides available for use. This programme does not aim to replace these
resources, but rather, to supplement them in a manner that will assist teachers to deliver high
quality Physical Sciences lessons.
Essentially, this programme aims to provide targeted support to teachers by doing the following:
1. Clarifying and explaining key concepts.
2. Clarifying and explaining possible misconceptions.
3. Providing worked examples of questions at an introductory level.
4. Providing worked examples of questions at a challenge level.
5. Providing the key teaching points to help learners deal with questions at challenge level.
6. Providing worksheet examples and corresponding memoranda for each topic.
7. Providing a Planner & Tracker that helps teachers to plan their lessons for a topic, and track
their progress, pacing and curriculum coverage.
8. Providing videos of formal assessment practicals, together with worksheets and
memoranda.
9. Providing guidance on how to structure formal assessment tasks.
10. Providing a ‘bank’ of questions and memoranda that may be used to structure formal
assessment tasks.
11. Providing a set of posters with key information to display in the classroom.
4
Grade 11 PHYSICAL SCIENCES Term 2
PROGRAMME ORIENTATION
CONTENT BOOKLET: TARGETED SUPPORT
1. The booklet starts with a contents page that lists all the topics for the term.
2. Every topic begins with a general introduction to the topic that states how long the topic
runs for and the value of the topic in the final exam. It also gives a general idea of what is
covered in the topic, and why this is important for our everyday lives.
3. This is followed by a list of requirements for the teacher and the learner. Try to ensure
that you have all requirements on hand for the topic, and that your learners always have
their requirements ready for each lesson. This is a simple classroom management practise
that can improve your time-on-task and curriculum coverage significantly!
4. Next, you will see a sequential table that shows the prior knowledge required for this topic,
the current knowledge and skills that will be covered, and how this topic will be built on in
future years. Use this table to give learners an informal quiz to test their prior knowledge.
If learners are clearly lacking in the knowledge and skills required, you may need to take a
lesson to cover some of the essential content and skills. It is also useful to see what you are
preparing learners for in the years to follow, by closely examining the ‘looking forward’ column.
5. This is followed by a glossary of terms, together with an explanation of each term. It is a
good idea to display these words and their definitions somewhere in the classroom, for the
duration of the topic. It is also a good idea to allow learners some time to copy down these
definitions into their books. You must explicitly teach the words and their meanings as and
when you encounter these words in the topic.
Once you have taught a new word or phrase, try to use it frequently in statements and
questions. It takes the average person 20 – 25 authentic encounters with a new word to
fully adopt it and make it their own.
6. Next, there are some very brief notes about the assessment of this topic. This just informs
you of when the topic will be assessed, and of the kinds of questions that are usually asked.
Assessment is dealt with in detail in the Assessment Booklet.
7. The next item is very useful and important. It is a table showing the breakdown of the
topic and the targeted support offered.
This table lists the sub topic, the classroom time allocation for the sub topic, and the
CAPS page reference.
The table also clearly states the targeted support that is offered in this booklet. You will
see that there are three main kinds of support offered:
a. Key concepts are clarified and explained.
b. Possible misconceptions are clarified and explained.
c. Questions are modelled and practised at different levels (introductory level and
challenge level).
Grade 11 PHYSICAL SCIENCES Term 2
5
PROGRAMME ORIENTATION
8. After this introduction, the targeted support for each sub topic commences. This
generally follows the same routine:
a. A key concept or key concepts are clarified and explained. It may be useful for
you to work through this carefully with learners, and do any demonstrations that are
included.
b. Questions related to the key concepts are worked and explained.
• These questions may be done at introductory level, at challenge level, or both.
• It is important to expose learners to challenge level questions, as this is often
how questions are presented in exams.
• These questions also challenge learners to apply what they have learnt about key
concepts. Learners are, essentially, challenged to think at a critical and analytical
level when solving these problems.
• Please note that when calculations are done at challenge level, the key teaching
points are identified.
• Make sure that you effectively share these key teaching points with learners, as
this can make all the difference as to whether learners cope with challenge level
questions or not.
c. At key points in the topic, checkpoints are introduced.
• These checkpoints involve asking learners questions to check that they
understand everything to that point.
• The checkpoints also refer to a worksheet activity that is included in the Worksheet
Booklet.
• Use checkpoints to ascertain whether more consolidation must be done, or if your
learners are ready to move to the next key concept.
9. Every topic ends with a consolidation exercise in the Worksheet Booklet. This exercise is
not scaffolded as a test, it is just a consolidation of everything covered in this programme for
that topic.
10. Finally, a section on additional reading / viewing rounds off every topic. This is a series
of web links related to the topic. Please visit these links to learn more about the topic, and
to discover interesting video clips, tutorials and other items that you may want to share with
your learners.
6
Grade 11 PHYSICAL SCIENCES Term 2
PROGRAMME ORIENTATION
THE WORKSHEET BOOKLET
1. The Worksheet Booklet has different worksheets and corresponding memoranda for each
topic.
2. First, there is a practise worksheet, with questions that learners must complete during the
topic. These are referred to in the checkpoints.
3. Once learners have completed these calculations, it is important to mark their work, using
the memorandum supplied. Either do this together as a whole class, or display copies of
the memorandum around the classroom, in spaces where learners can go and mark their
work for themselves.
4. It is important that learners see how marks are allocated in the memorandum, so that they
fully understand how to answer questions in tests and exams.
5. At the end of each topic, there is a consolidation worksheet and memorandum. This
worksheet is a consolidation exercise of all the calculations covered in the topic. The
consolidation worksheet is NOT scaffolded and it not designed to be used as a formal test.
The level of the worksheet will be too high to be used as a test.
6. Again, it is important for learners to mark their work, and to understand how marks are
allocated for each question.
7. Please remember that these worksheets do not replace textbook activities. Rather, they
supplement and extend the activities that are offered in the textbook.
THE PLANNER & TRACKER
1. The Planner & Tracker is a useful tool that will help you to effectively plan your teaching
programme to ensure that it is CAPS compliant.
2. The Planner & Tracker has a section for every approved textbook, so that regardless of the
textbook that you use, you will be able to use this tool.
3. It also has space for you to record all lessons completed, which effectively allows you to
monitor your curriculum coverage and pacing.
4. In addition, there is space for you to reflect on your progress and challenges at the end of
each week.
5. At the end of the Planner & Tracker, you will find a series of resources that may be useful to
you when teaching.
6. You will also find a sample formal assessment and memorandum.
Grade 11 PHYSICAL SCIENCES Term 2
7
PROGRAMME ORIENTATION
THE PRACTICALS BOOKLET AND VIDEOS
1. The following practicals must be completed as part of the formal assessment programme:
a. Grade 10 Term 1: Heating and cooling curve of water
b. Grade 10 Term 2: Electric circuits with resistors in series and parallel - measuring
potential difference and current
c. Grade 10 Term 3: Acceleration
d. Grade 11 Term 1: Relationship between force and acceleration
e. Grade 11 Term 2: The effects of intermolecular forces on: BP, MP, surface tension,
solubility, capillarity
f.
Grade 12 Term 1: Preparation of esters
g. Grade 12 Term 2: 1) Titration of oxalic acid against sodium hydroxide
i.
2) Conservation of linear momentum
h. Grade 12 Term 3: a) Determine the internal resistance of a battery
b) Set up a series-parallel network with known resistor. Determine the equivalent
resistance using an ammeter and a voltmeter and compare with the theoretical
value.
2. Videos of all the listed practicals are supplied as part of this programme.
3. These videos should ideally be used as a teacher’s guide. After watching the video, set up
and complete the practical with your learners. However, if this is not possible, then try to
show the video to your learners and allow them to record and analyse results on their own.
4. The videos should be used in conjunction with the practical worksheets. Learners should
complete the worksheet whilst watching the video.
THE POSTERS
1. Every FET Physical Sciences teacher will be given the following set of five posters to
display in the classroom:
8
a.
Periodic Table
b.
Chemistry Data Sheet
c.
Physics Data Sheet Part 1
d.
Physics Data Sheet Part 2
e.
Chemistry Half Reactions
Grade 11 PHYSICAL SCIENCES Term 2
PROGRAMME ORIENTATION
2. Please note that you will only be given these videos and posters once.
a.
Make sure you store the videos safely.
b.
It is also important for you to make these posters as durable as possible. Do this by:
•
Writing your name on all posters
•
Laminating posters, or covering them in contact paper
3. Have a dedicated wall or notice board in your classroom for Physical Sciences, per grade:
•
Use this space to display the posters
•
Display definitions and laws
•
Display any additional relevant or interesting articles or illustrations
•
Try to make this an attractive and interesting space
THE ASSESSMENT BOOKLET
1. A separate Assessment Booklet is provided for Grade 10, Grade 11 and Grade 12.
2. These booklets first show you how to structure the formal assessment tasks for each term,
according to CAPS requirements.
3. Next, the booklets provide you with a ‘bank’ of sample assessment questions for each topic.
4. This is followed by the memoranda for all the different questions that details the allocation
of marks.
5. This booklet gives you all the support required to structure and design different tests and
exams correctly.
Grade 11 PHYSICAL SCIENCES Term 2
9
PROGRAMME ORIENTATION
PHYSICAL SCIENCES PLANNING AND PREPARATION
1. Get into the habit of planning every topic by using the following documents together:
a. The Physical Sciences Planner & Tracker
b. The Content Booklet: Targeted Support
c. The Worksheet Booklet
d. The Practicals Booklet and Videos
e. Your Textbook
2. Planning should always be done well in advance. This gives you the opportunity to not only
feel well prepared but also to ask a colleague for help if any problems arise.
3. Follow these steps as you plan to teach a topic:
a. Turn to the relevant section in the Planner & Tracker for your textbook.
• Look through the breakdown of lessons for the topic.
• In pencil, fill in the dates that you plan to teach each lesson. This will help with
your sequencing.
b. Next, look at the topic in the Content Booklet: Targeted Support.
• Read through all the introduction points, including the table that shows the
breakdown of lessons, and the targeted support offered.
• Take note of the targeted support that is offered for each section.
• Read through the whole topic in the Content Booklet: Targeted Support.
• Complete all the examples in the Worksheet Booklet for the topic, including the
Consolidation Worksheet.
• Check your solutions against the memorandum.
• Make notes in your Planner & Tacker to show where you will include the targeted
support teaching and activities.
c. Now, turn to the relevant section in your Textbook.
• Read through each key concept in the Textbook.
• Complete as many examples as possible. This will also help in your teaching –
you will remember more points to share with the learners if you have done all of
the work yourself.
• Make careful notes in your Planner and Tracker of which sections and activities
you will teach from the Textbook, and which you will teach from the Content
Booklet: Targeted Support.
• It will strengthen your teaching to use a combination of the two resources, but be
careful not to leave anything out!
d. If the Topic includes one of the Practicals for formal assessment, then consult the
Practical Booklet and Video.
• Complete the worksheet for the practical, whilst watching the video.
•
10
•Try by all means to set up the practical and to conduct it with your learners.
However, if this is not possible, ensure that learners see the video and complete
the worksheet
Grade 11 PHYSICAL SCIENCES Term 2
PROGRAMME ORIENTATION
e.
f.
Document your lesson plans in the way that you feel most comfortable.
• You may like to write notes about your lesson plans in a notebook.
• You may like to use a standardised template for lesson planning. (A template is
provided at the end of this section).
• Remember to make notes about where you will use the textbook activities, and
where you will use the targeted support activities.
Ideally, Lesson Planning for a topic should include:
• Time to introduce the topic to learners
• Time to establish the learners’ prior knowledge
• If required, time to address critical gaps in learners’ prior knowledge
• Introduction of terminology (glossary words)
• Time to introduce and teach each key concept
• Time for learners to complete practise exercises for each key concept
• Time to correct and remediate each key concept
• Time for a consolidation worksheet
• Time to complete the required practicals
Note: Avoid giving learners an exercise to do that you haven’t already completed
yourself. This is useful for when the learners ask questions or get stuck on a question.
You will be ready to assist them immediately instead of wasting time reading the
question and working it out then.
PREPARATION AND ORGANISATION
1. Once you have completed your planning for a topic, you must make sure that you are
properly prepared and organised to teach it.
2. Do this by completing all the steps listed in the planning section, including completing all the
textbook and worksheet examples.
3. Have your lesson plans or teaching notes ready to work from.
4. Next, make sure that you have all resources required for the lesson.
5. Prepare your notice board for the topic, to give learners something visual to anchor their
learning on, and to generate interest around the topic.
6. Print copies of the worksheets for all learners.
Grade 11 PHYSICAL SCIENCES Term 2
11
PROGRAMME ORIENTATION
SAMPLE TEMPLATE FOR LESSON PLANNING
PHYSICAL SCIENCES LESSON PLAN
School
Teacher’s name
Grade
Term
Topic
Date
Lesson Duration
1. CONCEPTS AND SKILLS TO BE ACHIEVED:
By the end of the lesson learners should know and be able to:
2. RESOURCES REQUIRED:
3. HOMEWORK REVIEW / REFLECTION:
Exercises to be reviewed and notes:
12
Grade 11 PHYSICAL SCIENCES Term 2
PROGRAMME ORIENTATION
4. LESSON CONTENT / CONCEPT DEVELOPMENT
Explanation and examples to be done:
Grade 11 PHYSICAL SCIENCES Term 2
13
PROGRAMME ORIENTATION
5. CLASSWORK ACTIVITY
Resource 1
Page
Exercise
Resource 2
Page
Exercise
Notes:
6.HOMEWORK ALLOCATION
Resource 1
Page
Exercise
Resource 2
Page
Exercise
7. LESSON REFLECTION:
What went well:
What could have gone better:
14
Grade 11 PHYSICAL SCIENCES Term 2
PROGRAMME ORIENTATION
EXAM PREPARATION
Note: It is important to start preparing learners for their exam from the beginning of the term.
1. Make sure that your learners know exactly when their Physical Science exam will be written.
2. Ask learners to take out their exercise books, and to mark off what must be studied.
a. Go through all their written work, and get them to tick off the work that they must study
and practise.
b. If learners are missing notes, they must copy the missing work from another learner.
c. As you complete more work during the term that will be in the exam, tell learners to tick
it off and to add it to their study plans.
3. If necessary, help learners to work out a study schedule.
a. Estimate how long learners will need to study all the content required for the exam. This
will differ from grade to grade, and from learner to learner.
b. Be aware that some learners, even in the FET stage, have not yet developed these
planning skills.
c. Tell learners the number of hours that you think they need to study before the exam.
d. Break this down into the number of hours they should study each week.
e. Tell learners to think about their own lives and habits, and to work out when they have
time to study, and when they study best.
f.
They must then use all of this information to work out their study and revision plan.
Grade 11 PHYSICAL SCIENCES Term 2
15
PROGRAMME ORIENTATION
USEFUL REVISION RESOURCES
1. Assessment Booklets
a. THE Assessment Booklets that form part of this series may be used as a very useful
exam preparation tool.
b. These booklets include a ‘bank’ of questions for each topic at the different conceptual
levels.
c. If your province or district provides standardised tests and exams, use the questions in
this booklet at revision and exam preparation for learners.
d. Remember to carefully explain the question structure and meaning, together with the
mark allocation.
2. DBE Grade 12 ‘Mind the Gap’ Study Guides
a. Grade 12 learners can access the ‘Mind the Gap’ Study Guides on the DBE website:
https://www.education.gov.za/Curriculum/LearningandTeachingSupportMaterials(LTSM)/
MindtheGapStudyGuides.aspx
b. This series includes Grade 12 study guides for:
• Physical Science: Physics
•
Physical Science: Chemistry
c. These guides include an overview of the Grade 12 exam structures, useful study
techniques, a guide to questions types, a comprehensive list of question words / terms,
as well as a summary of key content and skills.
d. Consider downloading a copy of these guides, and making copies for Grade 12 learners
if possible.
e. Alternately, tell learners how to access this useful resource.
3. Vodacom e-school
a. If learners have a Vodacom number, they are eligible to use the Vodacom e-school as
a free service, i.e. no data costs: http://www.vodacom.co.za/vodacom/test-templates/
eschool-two
b. This e-school includes Physical Science lessons as part of its curriculum.
c. Tell learners how to access this useful resource.
16
Grade 11 PHYSICAL SCIENCES Term 2
TOPIC 5: Geometrical Optics
A
INTRODUCTION
•
This topic runs for 10 hours.
•
For guidance on how to break down this topic into lessons, please consult the NECT
Planner & Tracker.
•
Energy forms part of the content area Waves, Sound & Light (Physics).
•
Waves, Sound & Light counts as 21,3% in the final exam.
•
Geometrical optics counts approximately 12% to 16% of the final examination.
•
This is an enjoyable section, with some relatively easy experiments, some challenging
calculations, but with a limited number of equations, which makes it easier for the
learners.
CLASSROOM REQUIREMENTS FOR THE TEACHER
1. Chalkboard.
2. Chalk.
3. Grade 11 Physics Examination Data Sheet.
4. Highly recommended: Ray box; rectangular glass block, glass blocks of other shapes,
water, paper, pencil, ruler, protractor. If you do not have a ray box, a laser pointer works
very well instead.
CLASSROOM REQUIREMENTS FOR THE LEARNER
1. A4, 3 Quire exercise book, for notes and exercises.
2. Scientific calculator – Sharp or Casio calculators are highly recommended. Ensure that
these are set to ‘degrees’, not radians or grads.
3. Pen.
4. Additional paper.
5. Pencil and ruler.
6. Protractor.
Grade 11 PHYSICAL SCIENCES Term 2
17
TOPIC
5: Geometrical
TOPIC:
Whatever
LESSON: Optics
whatever
B
SEQUENTIAL TABLE
PRIOR KNOWLEDGE
CURRENT
Grade 10
Grade 11
Grade 12
•
Transverse pulses.
•
Geometrical Optics.
•
•
Transverse waves.
•
2D & 3D wavefronts.
•
Longitudinal waves.
•
Sound.
•
Electromagnetic
radiation.
18
LOOKING FORWARD
Grade 11 PHYSICAL SCIENCES Term 2
Doppler effect.
TOPIC 5: Geometrical Optics
C
GLOSSARY OF TERMS
TERM
DEFINITION
Law of reflection
The angle of incidence equals the angle of reflection.
(from gr 10)
+ i = + r or i i = i r
Also, the incident ray, the reflected ray and the normal all lie on the
same plane.
The speed of light
The speed of light is constant in a medium and has a maximum value
(c)
of 3×10 8 m·s -1
Refraction
The change of direction of a light ray because its speed changes
when it passes from one medium into another. (There are equivalent
definitions – but all have three parts i) change in in direction ii)
change in speed iii) change in medium.)
Refractive index ( n )
Optical density
c
n= v
An indication of the ease (speed) with which light travels through
a medium. (Note that this is not the same as, or related to, density
m
( V ).
Normal
The line perpendicular to the surface.
Angle of incidence
The angle between the incident ray and the normal.
Angle of refraction
The angle between the refracted ray and the normal.
Snell’s Law
Critical angle
n1 sin i1 = n2 sin i2
The angle of incidence which will give an angle of refraction of 90°
and the refracted ray is parallel to the boundary between the media.
Medium
The substance through which an energy form (e.g. a wave) passes.
The plural is mediums or media.
Transparent medium
A medium through which light can travel.
Opaque medium
A medium through which light cannot travel
Reflection (from gr 10)
When all or part of a pulse or wave changes direction at a boundary
between two media and returns into the original medium.
Total internal
When light in a medium of higher optical density reflects off a
reflection
boundary with no refraction occurring.
Grade 11 PHYSICAL SCIENCES Term 2
19
TOPIC
5: Geometrical
TOPIC:
Whatever
LESSON: Optics
whatever
D
ASSESSMENT OF THIS TOPIC
•
This topic is assessed through class tests and/or in the Term 4 examination.
•
There may be multiple-choice type questions, match the phrase type questions, or
problems to solve, where the learners are expected to show their method, give some
explanation and/or write down definitions or laws.
•
20
The determination of critical angle is a recommended informal experiment.
Grade 11 PHYSICAL SCIENCES Term 2
Grade 11 PHYSICAL SCIENCES Term 2
Critical
3 hours
reflection
total internal
angle and
Snell’s Law
Refraction
3 hours
4 hours
SUB TOPIC
77
77
76
CAPS PAGE
NUMBER
c
b. Challenge level calculations involving n1 sin i1 = n2 sin 90 .
a. Introduction level calculations involving n1 sin i1 = n2 sin 90.
2. Calculations, questions and ray diagrams are modelled and practised at different levels:
a. Total internal reflection
1. Key concepts and possible misconceptions are clarified and explained:
b. Challenge level calculations involving n1 sin i1 = n2 sin i2 ; ray diagrams and questions
and questions
a. Introduction level calculations involving n1 sin i1 = n2 sin i2 ; introductory ray diagrams
2. Calculations, questions and ray diagrams are modelled and practised at different levels:
a. Snell’s law
1. Key concepts and possible misconceptions are clarified and explained:
a. Introduction level calculations involving n = v ; introductory ray diagrams and questions
c
b. Challenge level calculations involving n = v ; ray diagrams and questions
2. Calculations, questions and ray diagrams are modelled and practised at different levels:
c. Optical density and refractive index
b. Refraction
a. The speed of light
1. Key concepts and possible misconceptions are clarified and explained:
TARGETED SUPPORT OFFERED
For further guidance on full lesson planning, please consult CAPS, the NECT Planner & Tracker and the textbook.
•
TIME
ALLOCATION
Please note that this booklet does not address the full topic – only targeted support related to common challenges is offered.
E
•
TOPIC:
Whatever
LESSON: Optics
whatever
TOPIC
5: Geometrical
BREAKDOWN OF TOPIC AND TARGETED SUPPORT OFFERED
21
TOPIC 5: Geometrical Optics
F
TARGETED SUPPORT PER SUB TOPIC
1.
REFRACTION
INTRODUCTION
Before starting refraction, reflection and the law of reflection is revised. While both reflection
and refraction are wave properties, it is important to note that particles will undergo similar
effects. It is really diffraction and interference (see topic 6) that will prove the wave nature of
light. This background may help prepare learners for the concepts in the photo-electric effect in
grade 12.
It is very useful to demonstrate this section both with practical demonstrations and experiments
(like a pencil in a glass of water) and with a ray box. When dealing with a ray box you will often
see both reflection and refraction occurring at the same time – and it is useful to prepare the
learners that this can happen. (Sometimes learners think only the one of the other happens.) It
is useful to make the room as dark as possible when using a ray box. If you do not have access
to a ray box a ‘laser pointer’ can be used, often they work better in fact.
CONCEPT EXPLANATION AND CLARIFICATION: SPEED OF LIGHT
The speed of light in a vacuum is a constant, normally given as 3×10 8 m·s -1 . However, light
changes its speed when it changes media. So it is not actually correct to say that the ‘speed of
light’ is a constant.
CONCEPT EXPLANATION AND CLARIFICATION: REFRACTION
A ray of light will refract towards the normal when entering a more dense optical medium. A ray
of light along the normal will not refract. It can be useful to use an analogy here, like a lawn
mower going from a patch of short grass (medium 1) to longer grass (medium 2.) the wheel that
enters the long grass first is slowed, and so the direction of the lawn mower’s movement will
change ‘towards the normal.’ If both front wheels enter at the same time (movement along the
normal) they slow down equally and the direction of movement is unaffected, although the lawn
mower slows down.
It is important to note that with refraction the speed changes, but the frequency does not. This
means that the wavelength has changed. This is different to the Doppler effect (grade 12)
where the frequency changes, not the speed.
22
Grade 11 PHYSICAL SCIENCES Term 2
TOPIC 5: Geometrical Optics
CONCEPT EXPLANATION AND CLARIFICATION: OPTICAL DENSITY AND REFRACTIVE INDEX
Optical density is more of a qualitative comparative concept (glass is optically more dense
than water) while the refractive index is a quantitative measure of this. The higher a material’s
refractive index, the more optically dense it will be. It is important to know that optical density
is independent of physical density (the relationship between mass and volume.) For example,
sunflower oil (0,9 g.cm-3) is less dense than water (1,0 g.cm-3), but has a higher refractive index
(1,47) than water (1,33) and so sunflower oil is optically more dense.
INTRODUCTORY LEVEL QUESTIONS
a. These are the basic questions with recall of information and calculations that learners
will be required to perform at this stage in the topic.
b. These are the basic calculations that learners will be required to perform at this stage in
the topic.
c. Their purpose is to familiarise the learners with the equation, but not to change the
subject of the formula.
d. Introductory ray diagrams are modelled.
How to tackle these questions in the classroom:
•
Work through these examples with learners.
•
Explain each step of the calculation to the learners as you complete it on the
chalkboard.
•
Learners must copy the question as well as the solution into their workbook.
1. Define the term refraction.
Solution
The change of direction of a light ray because its speed changes when it passes from
one medium into another. (The definition must have three parts i) change in in direction ii)
change in speed iii) change in medium.)
2. The speed of light in a vacuum in various media is given in the table below:
MATERIAL
SPEED OF LIGHT ( m·s -1 )
Vacuum
3×108
Air
3×108
Water
2, 25×108
Glass
1, 97×108
Grade 11 PHYSICAL SCIENCES Term 2
23
TOPIC
5: Geometrical
TOPIC:
Whatever
LESSON: Optics
whatever
a. Does light slow down significantly when it enters our atmosphere?
b. Calculate the refractive index for water
c. Calculate the refractive index for glass
d. Which of the three materials (air, water, glass) has the highest optical density?
Solution:
a. No (in fact it decreases by about 90 km.s-1, a factor of
about 0,03%, which is insignificant.)
b. c = 3×10 8 m s -1; v = 2, 25×10 8 m s -1
c
Use the formula for n.
n= v
3×108
=
Substitute the values.
2, 25×108
= 1, 33 Calculate the answer. Ensure that the learners enter
the values correctly on their calculators (use the
‘exponent’ button. If they are making errors, it will be
more obvious in later calculations, if they have the
wrong power of 10.) There is no unit for this answer.
c.
c = 3×108 m s -1; v = 1, 97×108 m s -1
c
n = v The same steps as in part (b.) so the learners can work
more independently.
=
3×108
1, 97×108
Substitute the values.
= 1, 52 There is no unit for this answer. Ensure that the
answer is given to two decimal places.
d. Glass
The optical density is related to the refractive
m
index. However, you can point out that the density ( V )
is not the same as the optical density.
3. Complete the diagrams
a.
air
water
24
Grade 11 PHYSICAL SCIENCES Term 2
TOPIC 5: Geometrical Optics
b.
air
Glass block
Solution:
It is almost important to see that the ray
bends towards from the normal
as it enters the more optically
dense material
a.
air
water
b.
air
Glass block
The light ray bends away from
the normal as it enters the less
optically dense material.
CHALLENGE LEVEL QUESTIONS
a. Now that learners have mastered the basic questions, they are ready to deal with more
challenging questions.
b. These questions require learners to manipulate the equation to change the subject of the
formula.
How to tackle these questions in the classroom:
•
Work through these examples with learners.
•
Tell learners that this is a more challenging version of what they have been doing.
•
Write the first example on the chalkboard.
•
Ask learners to look at the example and see if they can work out what must be done /
what is different.
•
Discuss learners’ ideas, and ask probing questions to extend their answers.
•
Try to be positive in these interactions, to encourage critical thinking and questioning.
•
Ensure that learners copy down both the question and the solution into their workbooks.
Grade 11 PHYSICAL SCIENCES Term 2
25
TOPIC
5: Geometrical
TOPIC:
Whatever
LESSON: Optics
whatever
Key Teaching:
a. In these more challenging examples, learners must manipulate the data and/or change
the subject of the formula, to solve for speed of light in the medium.
b. It is often easier for learners to substitute the values into the equation first, for example:
c
n= v.
c. Once learners have done this, they should then change the subject of the formula.
4. The refractive index for paraffin is 1,44. What is the speed of light in paraffin?
Solution:
c = 3×108 m s -1; n = 1, 44
c
n= v
1, 44 =
Use the formula for n
3×108
v
Substitute the values, they can re-arrange and then substitute, or
substitute and then re-arrange, as done here.
108
v = 31×, 44
v = 2, 08×108 m s -1
Calculate the answer. Ensure that the learners enter the values
correctly on their calculators (use the ‘exponent’ button. If they
are making errors, they will have the wrong power of 10.) Ensure
that answer is quoted in scientific notation to 2 decimal places.
Use the SI unit for the answer.
5. The refractive index for water is 1,33 and for quartz is 1,46. Complete the following ray
diagram:
water
quartz
Solution:
water
Because the second ray enters
along the normal, it does not bend.
quartz
26
Grade 11 PHYSICAL SCIENCES Term 2
TOPIC 5: Geometrical Optics
CHECKPOINT
At this point in the topic, learners should have mastered:
1. The calculation of refractive index.
2. The manipulation of the equation to calculate one of the other variables in the
equation.
3. The drawing of ray diagrams.
Check learners’ understanding of these concepts by getting them to work through:
WORKSHEET PACK: GEOMETRICAL OPTICS: QUESTIONS 1-5
•
Check learners’ understanding by marking their work with reference to the
memorandum.
•
If you cannot photocopy the memorandum for each learner, make three or four copies
of it and place these on the walls of your classroom.
2.
•
Allow learners time to mark their own work.
•
Encourage the learners to learn from the mistakes they make.
SNELL’S LAW
This topic introduces an unusual relationship, which is neither directly proportional nor indirectly
proportional, but rather based on a trigonometric function. This relationship is not as easy for
the learners to see, so if the angle of incidence is halved, the angle of refraction does not halve,
but it does decrease. Further, the learners must be reminded to ensure that their calculators are
on “degree” mode (not radian or gradient).
Grade 11 PHYSICAL SCIENCES Term 2
27
TOPIC 5: Geometrical Optics
INTRODUCTORY LEVEL QUESTIONS AND CALCULATIONS
a. These are the basic questions with recall of information and calculations that learners will
be required to perform at this stage in the topic.
b. These are the basic calculations that learners will be required to perform at this stage in
the topic.
How to tackle these questions in the classroom:
•
Work through these examples with learners.
•
Explain each step of the calculation to the learners as you complete it on the chalkboard.
•
Learners must copy the question as well as the solution into their workbook.
6. Light goes from air (refractive index of 1,00) into water (refractive index on 1,33). The angle
of refraction is 17°, what was the angle of incidence.
Solution:
n1 = 1,00 (air);
n2 = 1,33 (water);
θ2 = 17°;
θ1 = ?
n1 sin i1 = n2 sin i2
Use the correct formula.
1, 00× sin i1 = 1, 33× sin 17c
Substitute values
sin i1 = 1, 33×0, 2923
Ensure that they get the same value for sin17° on their
calculators
sin i1 = 0, 3889
Simplify
i1 = 22, 88c
Use the “shift” “sin” and “answer” buttons
7. A ray of light, at an angle of incidence of 35°, goes from sunflower oil to air (refractive
index =1,00) at a refracted angle of 57,5°. What is the refractive index of the sunflower oil?
Solution:
i1 = 35c; i2 = 5c7, 5; n = 1, 00;; n = ?
2
28
1
n1 sin i1 = n2 sin i2
Use the correct formula
n1 sin 35 = 1, 00× sin 57, 5
Substitute the values
n1 ×0, 574 = 0, 843
Simplify
Grade 11 PHYSICAL SCIENCES Term 2
TOPIC 5: Geometrical Optics
0, 843
n1 = 0, 574
There is no unit for this answer.
= 1, 47
8. Complete the diagrams
a.
b.
air
Glass
block
air
air
Glass
block
Solution:
a.
It is important to see that the ray bends towards
the normal as it enters the more optically dense
material, and away from the normal as it exits.
air
Glass
block
b.
Because the block has parallel sides, the
air
incident and emergent rays are parallel.
Again, the ray bends towards the normal as it
enters the more optically dense material, and
away from the normal as it exits. Because the
air
Glass
block
block doesn’t have parallel sides, the incident
and emergent rays are not parallel.
Grade 11 PHYSICAL SCIENCES Term 2
29
TOPIC 5: Geometrical Optics
CHALLENGE LEVEL QUESTIONS
a. Now that learners have mastered the basic calculations and ray diagrams, they are ready
to deal with more challenging questions.
b. These questions require learners to manipulate more data.
How to tackle these questions in the classroom:
•
Work through these examples with learners.
•
Tell learners that this is a more challenging version of what they have been doing.
•
Write the first example on the chalkboard.
•
Ask learners to look at the example and see if they can work out what must be done /
what is different.
•
Discuss learners’ ideas, and ask probing questions to extend their answers.
•
Try to be positive in these interactions, to encourage critical thinking and questioning.
•
Ensure that learners copy down both the question and the solution into their workbooks.
Key Teaching:
a. In these more challenging examples, learners must manipulate the data and/or change
the subject of the formula, to solve for mass, or the change in height.
b. It is often easier for learners to substitute the values into the equation first, for example:
n1 sin i1 = n2 sin i2 .
c. Once learners have done this, they should then change the subject of the formula.
9. The refractive index for paraffin is 1,44 and for water it is 1,33.
a. If light goes from paraffin to water with an incident angle of 45°, what is the angle of
refraction?
b. If light goes from water to paraffin with an incident angle of 40°, what is the angle of
refraction?
30
Grade 11 PHYSICAL SCIENCES Term 2
TOPIC 5: Geometrical Optics
Solution:
a. i1 = 45c; i2 = ?; n1 = 1, 33; n2 = 1, 44
n1 sin i1 = n2 sin i2
Use the correct formula
1, 33× sin 45 = 1, 44× sin i
Substitute the values
0, 940 = 1, 44 sin i
Simplify
0, 940
sin i = 1, 44
sin i = 0, 277
i = 16, 13°
b. i1 = 40c; i2 = ?; n1 = 1, 44; n2 = 1, 33
n1 sin i1 = n2 sin i2
Use the correct formula
1, 44× sin 40 = 1, 33× sin i
Substitute the values
0, 9256 = 1, 33 sin i
Simplify
0, 926
sin i = 1, 33
sin i = 0, 696
i = 44, 10°
It is important to see that in a.) the angle of refraction
was smaller than the incident angle, but greater in b.)
10. a. Complete the following ray diagram:
Glass
block
O
b. The ray does not bend when it enters the semi-circular block. What does this tell you
about the angle of incidence, and the point O?
Grade 11 PHYSICAL SCIENCES Term 2
31
TOPIC 5: Geometrical Optics
Solution:
a.
Glass
block
O
b. The angle of incidence is zero (0°)
Otherwise the ray would bend towards
the normal.
The point O is the centre of the If the incident ray is along the normal,
diameter of the circle. the ‘refracted’ ray in the block must
be along a radius of the circle and so
O must be the centre.
CHECKPOINT
At this point in the topic, learners should have mastered:
1. The calculations involving Snell’s law.
2. Drawing of ray diagrams.
Check learners’ understanding of these concepts by getting them to work through:
WORKSHEET PACK: GEOMETRICAL OPTICS: QUESTIONS 6-7
•
Check learners’ understanding by marking their work with reference to the
memorandum.
•
If you cannot photocopy the memorandum for each learner, make three or four copies
of it and place these on the walls of your classroom.
32
•
Allow learners time to mark their own work.
•
Encourage the learners to learn from the mistakes they make.
Grade 11 PHYSICAL SCIENCES Term 2
TOPIC 5: Geometrical Optics
3.
CRITICAL ANGLE AND TOTAL INTERNAL REFLECTION
INTRODUCTION
This section provides an easy and enjoyable experiment for informal assessment. For
extension, you could ask the more able learners to compare the calculated values (from Snell’s
Law) to the measured values from the experiment.
CONCEPT EXPLANATION AND CLARIFICATION: TOTAL INTERNAL REFLECTION
If a ray of light enters a medium with a lower refractive index (less optically dense), it bends
away from the normal. However, the angle of refraction normally cannot be greater than 90°,
because then it has not exited or refracted. Hence, as the angle of incidence increases, there
will come a stage when there is no refraction and only reflection (total internal reflection). Total,
because all the light is reflected, internal, because the ray remains inside the more optically
dense material.
Please note that in these experiments there will be both reflection and refraction, with the
reflected ray becoming more dominant as the angle of incidence increases. The reflected ray
will obey the law of reflection and the refracted ray will obey Snell’s Law until θ=90°, after which
the law can no longer apply.
Total internal reflection has many uses, especially in high speed communication (optical fibres/
cables.)
INTRODUCTORY LEVEL QUESTIONS
a. The basic questions are to ensure that the learners understand the concept of total
internal reflection and the conditions required for total internal reflection to occur.
b. These are the basic calculations that learners will be required to perform at this stage in
the topic.
How to tackle these questions in the classroom:
•
Work through these examples with learners.
•
Explain each step of the calculation to the learners as you complete it on the chalkboard.
•
Learners must copy the question as well as the solution into their workbook.
Grade 11 PHYSICAL SCIENCES Term 2
33
TOPIC 5: Geometrical Optics
3. A ray of light is going from water to air, as shown in the diagram.
air
water
The angle of refraction is 90°.
a. What is the angle of incidence called?
b. What happens if the angle of incidence is increased?
c. What are the conditions that are required for this total internal reflection to occur?
Solution:
a. The critical angle
b. Total internal reflection
c. Light goes from more optically dense to less optically dense material (or from higher to
lower refractive index); the angle of incidence is greater than the critical angle.
4. Light travels from a diamond (refractive index =2,42) to air (refractive index =1,00). What is
the maximum that the angle of incidence can be before total internal reflection occurs?
Solution:
i1 = ?; i2 = 90°; n1 = 2, 42; n2 = 1, 00
Note that the angle of refraction is 90°.
n1 sin i1 = n2 sin i2
Use the correct formula.
2, 42× sin i = 1, 00× sin 90°
Substitute the values.
1, 00
sin i = 2, 42
Simplify.
i = 24, 41
This small critical angle is part of the reason
that diamonds have their sparkle.
34
Grade 11 PHYSICAL SCIENCES Term 2
TOPIC 5: Geometrical Optics
CHALLENGE LEVEL QUESTIONS
a. Now that learners have mastered the basic calculations, they are ready to deal with more
challenging questions.
b. These questions require learners to manipulate the equation to change the subject of the
formula.
How to tackle these questions in the classroom:
•
Work through these examples with learners.
•
Tell learners that this is a more challenging version of what they have been doing.
•
Write the first example on the chalkboard.
•
Ask learners to look at the example and see if they can work out what must be done /
what is different.
•
Discuss learners’ ideas, and ask probing questions to extend their answers.
•
Try to be positive in these interactions, to encourage critical thinking and questioning.
•
Ensure that learners copy down both the question and the solution into their workbooks.
Key Teaching:
a. In these more challenging examples, learners must manipulate the data and/or change
the subject of the formula, to solve for mass, or the change in height.
b. It is often easier for learners to substitute the values into the equation first, for example:
n1 sin i1 = n2 sin 90 .
c. Once learners have done this, they should then change the subject of the formula.
5. In the diagram below (not to scale), a ray of light is travelling from glass towards the
boundary with acetone
Acetone
n=1,36
25˚
Glass n=1,52
Grade 11 PHYSICAL SCIENCES Term 2
35
TOPIC
5: Geometrical
TOPIC:
Whatever
LESSON: Optics
whatever
a. Write down the equation for Snell’s Law.
b. Calculate the critical angle for light going from glass into ice.
c. The angle of incidence is 25°. Copy and complete the ray diagram for the ray at the
boundary of the glass and acetone.
d. How does the speed of light in the glass compare to speed of light in acetone?
Solution:
a. n1 sin i1 = n2 sin i2
b. i1 = ?; i2 = 90°; n1 = 1, 52; n2 = 1, 36
Note that the angle of refraction is 90°.
n1 sin i1 = n2 sin i2
Use the correct formula.
1, 52× sin i = 1, 36× sin 90°
Substitute the values.
136
sin i = 1, 52
Simplify.
i = 63, 5°
c.
Acetone
n=1,36
25˚
›25˚
Glass n=1,52
d. Light travels slower in glass.
36
Grade 11 PHYSICAL SCIENCES Term 2
TOPIC:
Whatever
LESSON: Optics
whatever
TOPIC
5: Geometrical
CHECKPOINT
At this point in the topic, learners should have mastered:
a. The calculation of critical angle
b. The drawing of ray diagrams with critical angles
c. The practical application of total internal reflection, especially in optical fibres.
Check learners’ understanding of these concepts by getting them to work through:
WORKSHEET PACK: GEOMETRICAL OPTICS WORKSHEET: QUESTIONS 8-9
•
Check learners’ understanding by marking their work with reference to the
memorandum.
•
If you cannot photocopy the memorandum for each learner, make three or four
copies of it and place these on the walls of your classroom.
•
Allow learners time to mark their own work.
•
Encourage the learners to learn from the mistakes they make.
CONSOLIDATION
•
Learners can consolidate their learning by completing; Worksheet Pack: Geometrical
Optics: Consolidation Exercise.
•
Photocopy the exercise sheet for the learners. If that is not possible, learners will need to
copy the questions from the board before attempting to answer them.
•
The consolidation worksheet should be marked by the teacher so that she/he is aware of
each learner’s progress in this topic.
•
Please remember that further consolidation should also be done by completing the
examples available in the textbook.
•
It is important to note that this consolidation exercise is NOT scaffolded.
•
It should not be administered as a test, as the level of the work may be too high to
in its entirety.
Grade 11 PHYSICAL SCIENCES Term 2
37
TOPIC:
TOPIC
Whatever
5: Geometrical
LESSON: Optics
whatever
ADDITIONAL VIEWING / READING
In addition, further viewing or reading on this topic is available through the following web links:
1. https://www.youtube.com/watch?v=fjv6gWj1hx4
Video of refraction experiment with ray box and ripple tanks (about 2 min 30 s)
2. https://www.youtube.com/watch?v=XTMbYDrMr0w
A useful video to show how to draw ray diagrams from a ray box experiment (about
3 min 30 s)
3. https://www.youtube.com/watch?v=yfawFJCRDSE
Video showing a Snell’s Law experiment (2 min 55 s.) You can use the measurements
to draw up a table and do the analysis of the data.
4. https://www.youtube.com/watch?v=NAaHPRsveJk
A silent video showing a critical angle experiment (1 min 43 s). You can use the
measurements to draw up a table and do the analysis of the data.
38
Grade 11 PHYSICAL SCIENCES Term 2
TOPIC 6: 2D and 3D Wavefronts
A
INTRODUCTION
•
This topic runs for 3 hours.
•
For guidance on how to break down this topic into lessons, please consult the NECT
Planner & Tracker.
•
2D and 3D wavefronts form part of the content area Waves, Sound & Light (Physics).
•
Waves, Sound & Light counts as 21,3% in the final exam.
•
2D and 3D wavefronts counts approximately 7% of the final examination.
•
This section forms the basis of understanding diffraction and interference, which are the
properties of waves, and prove that light behaves as a wave. This can be compared with
the photo-electric effect in grade 12, where is it shown that light can also behave like a
particle.
CLASSROOM REQUIREMENTS FOR THE TEACHER
1. Chalkboard.
2. Chalk.
3. Grade 11 Physics Examination Data Sheet.
4. OPTIONAL: Ripple tank set up with a single slit and/or ray box and diffraction grating
with a very dark room.
5. PC or data projector to show videos of experiments (see recommended list at end.)
CLASSROOM REQUIREMENTS FOR THE LEARNER
1. A4, 3 Quire exercise book, for notes and exercises.
2. Scientific calculator – Sharp or Casio calculators are highly recommended.
3. Pen, pencil and eraser.
Grade 11 PHYSICAL SCIENCES Term 2
39
TOPICWhatever
6: 2D andLESSON:
3D Wavefronts
TOPIC:
whatever
B
SEQUENTIAL TABLE
PRIOR KNOWLEDGE
CURRENT
Grade 10
Grade 11
Grade 11-12
•
Transverse pulses.
•
•
Doppler effect
•
Transverse waves.
•
Longitudinal waves.
•
Sound.
•
Electromagnetic
•
Photoelectric affect
•
See above
Geometric Optics
(topic 5)
•
Refraction
•
Snell’s Law
•
Critical angles and total
internal reflection
radiation
40
LOOKING FORWARD
•
2D and 3D wavefronts
•
Diffraction
Grade 11 PHYSICAL SCIENCES Term 2
TOPIC:
whatever
TOPICWhatever
6: 2D andLESSON:
3D Wavefronts
C
GLOSSARY OF TERMS
Please note: The highlighted definitions and laws are ones that learners must be able to state
and are given in the CAPS document. For examination purposes, learners must know these
definitions and laws by heart, and must write them exactly as they appear here.
TERM
DEFINITION
Wavefront
An imaginary line that connects waves that are in phase
(e.g. all at the crest of their cycle.)
Huygens’ principle
Every point on a wavefront acts as the source of secondary
wavelets that spread out in the forward direction with the same
speed as the wave.
Diffraction
The ability of a wave to spread out in wavefronts as they pass
through a small aperture or around a sharp edge OR The
bending of a wave around an obstacle or the corners of a
narrow opening.
Superposition
Two (or more) waves that meet at the same point at the same
time.
Destructive interference
Two (or more) waves that are totally out of phase meet at a
point.
Constructive interference
Two (or more) waves that are exactly in phase meet at a point.
Nodal line
A line in an interference pattern where destructive interference
takes place.
Grade 11 PHYSICAL SCIENCES Term 2
41
TOPICWhatever
6: 2D andLESSON:
3D Wavefronts
TOPIC:
whatever
D
42
ASSESSMENT OF THIS TOPIC
•
In the midyear and final examinations
•
Possibly in a control test
Grade 11 PHYSICAL SCIENCES Term 2
SUB TOPIC
Diffraction
3 hours
78
CAPS PAGE NUMBER
Grade 11 PHYSICAL SCIENCES Term 2
with both water and light waves.
b. Challenge level questions applying the concepts to a wider context
interference, also diffraction and Huygens’ principle.
a. Introductory question on concepts, including a revision of
practised at different levels:
2. Calculations, questions and ray diagrams are modelled and
b. Diffraction
a. Huygens’ principle
explained:
1. Key concepts and possible misconceptions are clarified and
TARGETED SUPPORT OFFERED
For further guidance on full lesson planning, please consult CAPS, the NECT Planner & Tracker and the textbook.
•
TIME ALLOCATION
Please note that this booklet does not address the full topic – only targeted support related to common challenges is offered.
E
•
TOPIC:
whatever
TOPICWhatever
6: 2D andLESSON:
3D Wavefronts
BREAKDOWN OF TOPIC AND TARGETED SUPPORT OFFERED
43
TOPIC:
whatever
TOPICWhatever
6: 2D andLESSON:
3D Wavefronts
F
TARGETED SUPPORT PER SUB TOPIC
1.
2D AND 3D WAVEFRONTS
INTRODUCTION
In this topic, waves are typically depicted quite differently from how they are shown in
Geometric Optics. There, the emphasis was on ray diagrams and not on the ‘wave-nature’ of
the light ray. In this section, learners will examine the wave nature of the light, and view waves
both from a ‘side-view’ and look at wave patterns from ‘above.’ Making this difference explicit
will help some learners, especially the more advanced learners.
CONCEPT EXPLANATION AND CLARIFICATION:
Huygens’ Principle: each wave front is seen as being made up of an infinite number of miniwaves, each cancelling each other (by destructive interference) for most of the wave, but
reinforcing each other (by constructive interference) where they are in phase, giving rise to a
single wave front. Formally, this is stated as “every point on a wavefront acts as the source of
secondary wavelets that spread out in the forward direction with the same speed as the wave.”
However, its importance is seen when the wavelet is removed from an area, for example by
the wave going through a slit.
Diffraction: the spreading of a wave which has passed through an aperture, or past a sharp
edge. Diffraction gives rise to a typical diffraction pattern, which can be seen with both water
waves and light, and thus demonstrates the wave nature of light. The extent or degree of
diffraction depends upon both the wavelength and the width of the slit giving rise to the
diffraction. The degree of diffraction is directly proportional to the wavelength of the wave
and inversely proportional to the width of the slit. Different colours of light (with different
wavelengths) will thus show differing degrees of diffraction, with the colours with a longer
wavelength diffracting more.
44
Grade 11 PHYSICAL SCIENCES Term 2
TOPIC:
TOPICWhatever
6: 2D andLESSON:
3D Wavefronts
whatever
INTRODUCTORY LEVEL QUESTIONS
a. These questions help the learners to understand and memorise the basic concepts that
are required for this topic.
b. These are the basic calculations that learners will be required to perform at this stage in
the topic.
c. Their purpose is to familiarise the learners with the equation, but not to change the
subject of the formula.
How to tackle these questions in the classroom:
•
Work through these examples with learners.
•
Explain each step of the calculation to the learners as you complete it on the chalkboard.
•
Learners must copy the question as well as the solution into their workbook.
1. Consider the wave patterns given below:
a. Draw the resulting wave pattern from these two waves, which are in phase with
each other.
b. What is the interaction of these waves called?
Solution:
a. Although destructive and constructive inference are not directly examined in this
section, it is very useful to do some easy revision examples. These are needed
to explain Huygens’ principle, and especially the diffraction pattern of light. These
examples will help the learners to understand these concepts. Thus, the resultant
wave will be bigger than the other 2.
Grade 11 PHYSICAL SCIENCES Term 2
45
TOPICWhatever
6: 2D andLESSON:
3D Wavefronts
TOPIC:
whatever
b. Constructive interference
2. A wave passes through a narrow gap as pictured below.
a. Using the diagram above, explain the concept of diffraction
b. The wavelength of the incoming waves is decreased. Would the waves bend more or
less? Use a mathematical expression to explain your answer.
c. From the original diagram, the size of the gap is decreased. Would the waves bend
more or less? Use a mathematical expression to explain your answer.
Solution:
a. Diffraction is the bending of a wave around an obstacle or the corners of a narrow
opening. As the waves pass through the narrow gap the ‘ends’ of the wave start to
bend. This causes the wave to spread and to go into the area ‘behind’ the obstacle.
b. As wavelength decreases, the degree of diffraction decreases, so the waves bend less.
Degree of diffraction a
46
1
.
m
Grade 11 PHYSICAL SCIENCES Term 2
TOPIC:
whatever
TOPICWhatever
6: 2D andLESSON:
3D Wavefronts
c. If the width if the gap is decreased, the degree of diffraction increases. Thus, the waves
would bend more. Degree of diffraction a width .
3. Huygens stated that a wavefront can be considered to be made of an infinite number of
mini-wavelets, as pictured below.
Picture source https://www.ux1.eiu.edu/~cfadd/1160/Ch25WO/Huygn.html
a. Why are the circular waves not seen behind the wavefront?
b. How can these circular waves produce a straight wavefront?
c. How does this explain the bending of a wave around an edge?
Solution:
a. The wavelets have destructive interference everywhere behind the wavefront. Thus,
the wavelets ‘cancel’ each other out behind the wavefront and are not seen.
b. The wavefronts do not interfere with each other on the wavefront – thus it maintains its
shape (in this case from a straight source) giving a straight wavefront.
c. Every point on the wavefront is a wavelet. The wavelets destructively interfere with
each other except on the wavefront. However, when the wavefront passes through a
slit, the wavelets on each side are removed, which means that the wavelets spread out
and cause interference.
Grade 11 PHYSICAL SCIENCES Term 2
47
TOPICWhatever
6: 2D andLESSON:
3D Wavefronts
TOPIC:
whatever
CHALLENGE LEVEL QUESTIONS
a. Now that learners have mastered the basic questions and calculations, they are ready to
deal with more challenging questions.
b. These questions require learners to explain the concepts in a greater variety of contexts.
How to tackle these questions in the classroom:
•
Work through these examples with learners.
•
Tell learners that this is a more challenging version of what they have been doing.
•
Write the first example on the chalkboard.
•
Ask learners to look at the example and see if they can work out what must be done /
what is different.
•
Discuss learners’ ideas, and ask probing questions to extend their answers.
•
Try to be positive in these interactions, to encourage critical thinking and questioning.
•
Ensure that learners copy down both the question and the solution into their workbooks.
Key Teaching:
In these more challenging examples, learners must apply the concepts in a wider variety of
contexts.
4. Consider the two diffraction patterns for green and red light, respectively, given below. The
patterns were generated with the same diffraction grating.
green light
red light
a. What does the fact that light diffracts prove about the nature of light?
b. Compare the two diffraction patterns – how are they different?
c. In what ways are they the same?
d. What can you conclude about the wavelength of green light compared to the
wavelength of red light?
48
Grade 11 PHYSICAL SCIENCES Term 2
TOPIC:
whatever
TOPICWhatever
6: 2D andLESSON:
3D Wavefronts
Solution:
a. The diffraction of light shows that it has a wave nature.
b. The second diffraction pattern (red, the lower one) is wider and shows a greater degree
of diffraction.
c. They both have a central band and 3 bright bands on either side, which grow fainter as
they get further from the centre.
d. Green light has a shorter wavelength than red light (degree of diffraction a m. )
5. A learner conducts an experiment with light and obtains a diffraction pattern. How will the
pattern change if:
a. The wavelength of the waves is doubled?
b. The width of the gap is doubled?
c. Both the wavelength and the width are doubled?
Solution:
a. The diffraction will increase (double).
b. The diffraction will decrease (halve).
c. The diffraction will remain exactly the same (degree of diffraction a
m
width ).
6. A girl is standing in the corner of a room, cannot see the speaker in the room next door
through the door. But she can still hear the sound. Explain this observation.
Solution:
The sound will diffract as it passes through the doorway. However, light has a much, much
shorter wavelength than sound and so the diffraction of the light is negligible. The speaker
cannot be seen because there is no clear direct line from the girl through the door to the
speaker, but the sound bends to enable her to her the speaker.
Grade 11 PHYSICAL SCIENCES Term 2
49
TOPICWhatever
6: 2D andLESSON:
3D Wavefronts
TOPIC:
whatever
CHECKPOINT
At this point in the topic, learners should have mastered:
a. The factors affecting diffraction.
b. Huygens’ principle and how this can explain diffraction.
c. The application of diffraction to water waves (in a ripple tank), sound waves and light.
Check learners’ understanding of these concepts by getting them to work through:
WORKSHEET PACK: 2D AND 3D WAVEFRONTS: QUESTIONS 1-6
•
Check learners’ understanding by marking their work with reference to the
memorandum.
•
If you cannot photocopy the memorandum for each learner, make three or four copies
of it and place these on the walls of your classroom.
•
Allow learners time to mark their own work.
•
Encourage the learners to learn from the mistakes they make.
CONSOLIDATION
•
Learners can consolidate their learning by completing; Worksheet Pack: 2D and 3D
wavefronts: Consolidation Exercise.
•
Photocopy the exercise sheet for the learners. If that is not possible, learners will need to
copy the questions from the board before attempting to answer them.
•
The consolidation worksheet should be marked by the teacher so that she/he is aware of
each learner’s progress in this topic.
•
Please remember that further consolidation should also be done by completing the
examples available in the textbook.
•
It is important to note that this consolidation exercise is NOT scaffolded.
•
It should not be administered as a test, as the level of the work may be too high to
in its entirety.
50
Grade 11 PHYSICAL SCIENCES Term 2
TOPIC:
whatever
TOPICWhatever
6: 2D andLESSON:
3D Wavefronts
ADDITIONAL VIEWING / READING
In addition, further viewing or reading on this topic is available through the following web links:
1. https://www.youtube.com/watch?v=vqa4L0DuWbM
Mindset video 8 minutes 22 seconds.
2. https://www.siyavula.com/science/grade-11/06-2d-and-3d-wavefronts/06-2d-and-3dwavefronts-05.cnxmlplus
This explanation by Siyavula goes beyond the syllabus but is good further reading to give
extra background for a teacher.
3. https://www.youtube.com/watch?v=egRFqSKFmWQ
This shows single slit diffracting in a ripple tank. The 1st 1:45 is about single slits, and it
shows the effect very well, even showing nodal lines (best seen at about 1:27 and 1:35).
4. https://www.youtube.com/watch?v=RXMofhv3JwE
This video shows the results of single slit light of various widths and also for circular slits
(3:18).
Grade 11 PHYSICAL SCIENCES Term 2
51
TOPICTOPIC:
7: Ideal
Gases and
Thermal
properties
Whatever
LESSON:
whatever
A
INTRODUCTION
•
This topic runs for 8 hours.
•
For guidance on how to break down this topic into lessons, please consult the NECT
Planner & Tracker.
•
Energy forms part of the content area (Chemistry).
•
Matter & Materials counts as 15% in the final examinations.
•
The chemistry part of Matter & Materials (molecular structure, intermolecular forces,
and ideal gases) counts approximately 11 % of the final examinations, or 22 % of the
chemistry examination. Thus, Ideal gases will count about 13% of the chemistry paper.
CLASSROOM REQUIREMENTS FOR THE TEACHER
1. Chalkboard.
2. Chalk.
3. Grade 11 Chemistry Examination Data Sheet.
4. Optional Practical requirements: although optional it is highly recommended that some
of the experimental work is done. A Boyle’s law apparatus may be used, or Charles’ law
can be shown with a good, well-sealed graduated syringe and ice and water baths, with
a thermometer.
CLASSROOM REQUIREMENTS FOR THE LEARNER
1. A4, 3 Quire exercise book, for notes and exercises.
2. Scientific calculator – Sharp or Casio calculators are highly recommended.
3. Pen.
52
Grade 11 PHYSICAL SCIENCES Term 2
Whatever
LESSON:
whatever
TOPICTOPIC:
7: Ideal
Gases and
Thermal
properties
B
SEQUENTIAL TABLE
PRIOR KNOWLEDGE
CURRENT
LOOKING FORWARD
Grade 10
Grade 11
Grade 12
•
•
•
States of Matter and
Kinetic Molecular theory.
Ideal Gases.
Although not directly
Motion of particles:
related, many of the
kinetic theory of
kinetic theory concepts
gases
used here carry
•
Ideal gas law
forward into Rates of
•
Temperature and
Reactions and Chemical
heating, pressure
Equilibrium
•
Grade 11 PHYSICAL SCIENCES Term 2
53
TOPICTOPIC:
7: Ideal
Gases and
Thermal
properties
Whatever
LESSON:
whatever
C
GLOSSARY OF TERMS
Please note: The highlighted definitions and laws are ones that learners must be able to
state and are given in the CAPS document. For examination purposes, learners must know
these definitions and laws by heart, and must write them exactly as they appear here.
TERM
DEFINITION
Boyle’s Law
For a fixed amount of gas, at a constant temperature, volume is
inversely proportional to pressure.
Charles’ Law
For a fixed amount of gas, at a constant volume, pressure is inversely
proportional to absolute temperature.
Gay Lussac’s Law
For a fixed amount of gas, at a constant pressure, volume is inversely
proportional to absolute temperature.
The Ideal gas law
The amount of a gas is determined by its pressure, volume and
temperature. In symbols, PV = nRT.
Ideal gas
A gas which fulfils a number of assumptions and obeys the equation
PV = nRT.
Real gas
A gas that occurs in nature and will not obey PV =nRT, especially at
high pressure and low temperatures.
Kelvin temperature
0 K is absolute zero, and 273 K = 0°C; T K= t°C +273
particle
The smallest unit in a chemical reaction or physical process.
Pressure
Pressure arises from the collisions of the particles with the walls of
the container. It depends on the frequency of the collisions per unit
area
Temperature
A measure of hotness or coldness, usually measured with a
thermometer.
A measure of the average kinetic energy of the particles.
54
Grade 11 PHYSICAL SCIENCES Term 2
Whatever
LESSON:
whatever
TOPICTOPIC:
7: Ideal
Gases and
Thermal
properties
D
ASSESSMENT OF THIS TOPIC
•
This topic is assessed through class tests and/or in the Term 2 examination.
•
There may be multiple-choice type questions, match the phrase type questions, or
problems to solve, where the learners are expected to show their method, give some
explanation and/or write down definitions or laws.
•
There are several experiments available, and it is recommended that the Boyle’s law
experiment is done as an informal assessment.
Grade 11 PHYSICAL SCIENCES Term 2
55
TOPIC 7: Ideal Gases and Thermal properties
•
Please note that this booklet does not address the full topic – only targeted support related to common challenges is offered.
TARGETED SUPPORT OFFERED
For further guidance on full lesson planning, please consult CAPS, the NECT Planner & Tracker and the textbook.
SUB TOPIC
CAPS PAGE
NUMBER
1. Key concepts and possible misconceptions are clarified and explained:
81
P1 V1
P2 V2
T1 = T2
4. The relationship between temperature, pressure and the motion of the
particles is revised.
b. Challenge level calculations, based on PV = nRT and more difficult
P1 V1
P2 V2 .
T1 = T2
c. The conversion of units as needed.
a. Introductory calculations, largely derived from
3. Calculations are modelled and practised at different levels.
b. The importance of the kelvin scale of temperature.
a. The three gas laws, which can be combined into the Ideal gas law.
2. Key concepts and possible misconceptions are clarified and explained:
c. The relationship between pressure and the motion of the particles.
b. The relationship between temperature and the motion of the particles.
a. The ideal gas model, and scientific models in general.
79
particles:
Kinetic theory
of gases
Ideal gas law
Temperature
80
Motion of
•
TIME
ALLOCATION
1 hour
6 hours
1 hour
and heating,
pressure
Grade 11 PHYSICAL SCIENCES Term 2
56
BREAKDOWN OF TOPIC AND TARGETED SUPPORT OFFERED
E
TOPIC 7: Ideal Gases and Thermal properties
F
TARGETED SUPPORT PER SUB TOPIC
1.
MOTION OF PARTICLES: KINETIC THEORY OF GASES
INTRODUCTION TO THE ENTIRE TOPIC
These three sections (Motion of particles; Ideal gas law and temperature and heating, pressure)
must be taught in an integrated fashion.
This topic relates strongly back to the Kinetic theory of matter from earlier grades, and even to
Intermolecular forces from earlier in the grade 11 year. (Real gases deviate from ideal gases
when the intermolecular forces become significant).
This topic also allows for the differentiation in the learners’ minds between the sub-microscopic
world of particles (in this topic a particle is usually a molecule or the atom of a noble gas)
and the macroscopic world of our experience. For example, we experience temperature as a
perceived coldness or heat, but the explanation for that is found in the average kinetic energy
of the particles.
This section also allows learners to refine their idea of a scientific model. The Ideal gas is a
scientific model which is very useful and enables us to do a number of calculations. However,
the model has its limitations (such as conditions of low temperature and high pressure) when
the real gas will deviate from the predictions of the ideal gas model. It is important for the
learners to note that the model is not wrong, but rather that the limits of the model have been
exceeded.
This topic has place for doing good practical work, including analysis of data and graphing,
both very important skills for the final grade 12 examination. It may also be useful to point out
to learners the advantage of having directly proportional relationships. So, working in Kelvin in
P
P
Gay Lussac’s law (relationship of P to T) enables the direct proportionality 1 = 2 to be used.
T1 T2
Note: the CAPS document uses P as the abbreviation for pressure, but some textbooks use p.
We will use the CAPS notation.
CONCEPT EXPLANATION AND CLARIFICATION: MOTION OF PARTICLES: KINETIC THEORY OF GASES
This section uses the sub-microscopic world to explain real life phenomena. It is very useful
to distinguish clearly between macroscopic events (pressure, temperature) and the submicroscopic kinetic theory explanation. The learners can see and engage in the one world,
and have to imagine the other. If you have access to the internet, it is very useful to show them
animations, such as listed in the website(s) at the end of this module.
Grade 11 PHYSICAL SCIENCES Term 2
57
TOPIC 7: Ideal Gases and Thermal properties
Pressure is explained by the particles colliding with the walls of the container. Pressure will
be increased by increasing the frequency of those collisions (more collisions per second) or
the force exerted by the particles on the walls, which is related to their momentum (a greater
momentum means that as they change direction when bouncing off the walls, there is a greater
nett force exerted on the particles (Fnet = change in momentum/time) and by the particles on the
walls of the container. The average momentum of the particles is proportional to their average
kinetic energy, which is measured in the macroscopic world by temperature.
CONCEPT EXPLANATION AND CLARIFICATION: IDEAL AND REAL GASES
The idea of an ideal gas is a theoretical model, which enables us to make accurate predictions
about the behaviour of a gas. It makes certain assumptions, the most important of which are:
1. The particles are identical and are in constant motion. This assumption makes the
mathematics behind the ideal gas theory easier to work with, but doesn’t really affect the
learners’ understanding.
2. The gas particles are small and their volume is negligible. This is an important assumption –
it is true for real gases at high temperatures and low pressures.
3. There are no intermolecular forces between the particles and they move in a straight
line between collisions. The lack of intermolecular forces is true in real gases at high
temperatures and low pressures.
4. The collisions between the particles, or the particles and the walls of the container are
perfectly elastic i.e. there is no loss of total kinetic energy.
5. The gas fills the whole space available to it. This will be important in some calculations,
such as when a balloon or syringe expands.
The Ideal gas model works well at high temperatures and low pressures. The value of the
‘high’ temperature and ‘low’ pressure will depend on each gas. As long as a gas is quite far
from liquefying (this depends on temperature as well as pressure), it will behave ideally. A gas
will not behave like an ideal gas at low temperature and high pressure. There are two primary
reasons for this:
•
The intermolecular forces become significant and can no longer be ignored (which is
obviously what happens when a substance liquefies).
•
The volume of the particles becomes significant. The volume of the particles is most
significant at high pressures.
58
Grade 11 PHYSICAL SCIENCES Term 2
TOPIC 7: Ideal Gases and Thermal properties
CHALLENGE LEVEL QUESTIONS
a. These are the basic questions with recall of information that learners will be required to
perform at this stage in the topic.
b. Their purpose is to familiarise the learners with the assumptions and definitions used in
this section, but not to change the subject of the formula.
How to tackle these questions in the classroom:
•
Work through these examples with learners.
•
Explain each step of the calculation to the learners as you complete it on the chalkboard.
•
Learners must copy the question as well as the solution into their workbook.
1. State the assumptions of the Ideal gas model
Solution:
•
The particles are identical and are in constant motion.
•
The gas particles are small and their volume is negligible.
•
There are no intermolecular forces between the particles and they move in a straight line
between collisions.
•
The collisions between the particles, or the particles and the walls of the container are
perfectly elastic.
2. The temperature of a sample of gas is increased.
a. Explain, using the kinetic theory, what happens to the average speed of the molecules
of the gas.
b. State what happens to the pressure, assuming the volume of the container remains
constant.
c. Explain your answer to (b) above, in terms of the kinetic theory.
Solution:
a. The average speed of the molecules will increase. (This is because temperature is a
measure the average kinetic energy, which is
1
2
mv2)
Grade 11 PHYSICAL SCIENCES Term 2
59
TOPIC 7: Ideal Gases and Thermal properties
b. The pressure will increase.
c. The molecules will move more quickly, so they will collide with the walls of the
container more frequently (i.e. more collisions per unit time.) Also, because their
speed, on average, is higher, they will have a greater average momentum and change
in momentum - so exert a greater force of the walls of the container. (Note it is very
important that the learners understand that it is not sufficient to speak of the ‘number
of collisions’ but the ‘number of collisions per unit time’ or ‘frequency of collisions’ is
required. These ideas are also important in the Rate of reactions section in grade 12.)
CHALLENGE LEVEL QUESTIONS
a. Now that learners have mastered the basic questions, they are ready to deal with more
challenging questions.
b. These questions require learners to give explanations in greater detail.
How to tackle these questions in the classroom:
•
Work through these examples with learners.
•
Tell learners that this is a more challenging version of what they have been doing.
•
Write the first example on the chalkboard.
•
Ask learners to look at the example and see if they can work out what must be done /
what is different.
•
Discuss learners’ ideas, and ask probing questions to extend their answers.
•
Try to be positive in these interactions, to encourage critical thinking and questioning.
•
Ensure that learners copy down both the question and the solution into their workbooks.
Key Teaching:
a. In these more challenging examples, learners must see the limitations of scientific
models.
b. Learners also are encouraged to predict the cause of a scientific model not being valid
under certain conditions.
60
Grade 11 PHYSICAL SCIENCES Term 2
TOPIC 7: Ideal Gases and Thermal properties
3. The Ideal gas model is a simplification that we use in science.
a. Under what conditions will a real gas condense into a liquid?
b. Will a liquid behave like an ideal gas? Explain.
Solution:
a. Low temperature and high pressure.
b. No, except that both flow, otherwise they behave fairly differently.
4. The volume of an enclosed mass of gas is decreased.
a. Predict what will happen to the pressure of the gas.
b. Explain your answer to (a), using the kinetic theory.
Solution:
a. The pressure will increase.
b. Because the volume has decreased, the molecules have less space to move and so
they collide more frequently with the wall of the container. Thus, the pressure increases.
CHECKPOINT
At this point in the topic, learners should have mastered:
1. The ideas of the kinetic theory of matter for gases.
2. The relationship between temperature, pressure and the behaviour of the molecules.
Check learners’ understanding of these concepts by getting them to work through:
WORKSHEET PACK: IDEAL GASES AND THERMAL PROPERTIES WORKSHEET: QUESTIONS 1-2
•
Check learners’ understanding by marking their work with reference to the
memorandum.
•
If you cannot photocopy the memorandum for each learner, make three or four copies
of it and place these on the walls of your classroom.
•
Allow learners time to mark their own work.
•
Encourage the learners to learn from the mistakes they make.
Grade 11 PHYSICAL SCIENCES Term 2
61
TOPIC 7: Ideal Gases and Thermal properties
2.
IDEAL GAS LAWS
CONCEPT EXPLANATION AND CLARIFICATION: THE IDEAL GAS LAW
There are 3 gas laws, which can be combined into the ideal gas law, PV = nRT . The
units for these are interesting, in that temperature must always be measured in kelvin (K)
where 0 K = -273°C, but there is variance with the other physical quantities. If R is used,
then everything must be measured in SI units (Pa, m3, mol, K) but in an equation without R
consistent and appropriate units can be used. So, volume can be measured as dm3 or ml
or any appropriate unit, as long as the same unit is used for V1 and V2. But it may be better,
when using the ideal gas law equation, especially for the weaker learners, to select one set of
values for pressure and volume for this equation and say that learners must always convert to
these units first before using the equation. This is to prevent ‘mixing’ of incorrect units with one
another.
This is a section with strong ties to mathematical concepts such as graphs and the shapes of
graphs, direct proportionality and inverse proportionality. All of these proportions can be derived
from the Ideal gas law, or from the appropriate specific law. So, considering the relationship
between pressure and volume (all other variables will be kept constant, we get PV = k . If
this is plotted as a pressure against volume graph, we can easily see that the shape is a
hyperbola (like xy = k.) From this we can see that pressure is inversely proportional to volume
1
1
(P = V or P \ V ) . This means that if pressure doubles, volume halves (or vice-versa).
P1 V1
P2 V2
= T
A very useful form of the equation in solving problems is T
. This can be used in
1
2
almost any problem with ‘initial and final’ conditions, with the variable that doesn’t change
eliminated, as it is a constant.
Lastly, at least one of the gas laws should be used as the basis for an informal assessment
as a practical. Really good data can be obtained and, fairly often, questions will be set on the
basis of experimental data.
62
Grade 11 PHYSICAL SCIENCES Term 2
TOPIC 7: Ideal Gases and Thermal properties
CHALLENGE LEVEL QUESTIONS
a. These are the basic questions with recall of information and calculations that learners
will be required to perform at this stage in the topic.
b. These are the basic calculations that learners will be required to perform at this stage
in the topic.
c. Their purpose is to familiarise the learners with the equation.
How to tackle these questions in the classroom:
•
Work through these examples with learners.
•
Explain each step of the calculation to the learners as you complete it on the chalkboard.
•
Learners must copy the question as well as the solution into their workbook.
5. Which of the following statements is true for a real gas?
A
There are no forces of attraction between the particles.
B
Collisions between the particles are perfectly elastic.
C
All motion of particles ceases at 0 ˚C.
D
The particles have real volume.
Solution:
D – all the other statements (A-C) apply to ideal gases.
6. The kelvin temperature of 80 cm3 of gas is halved. What will the final volume (in cm3) of gas
be at the new temperature?
A
20
B
40
C
80
D
160
Grade 11 PHYSICAL SCIENCES Term 2
63
TOPICTOPIC:
7: Ideal
Gases and
Thermal
properties
Whatever
LESSON:
whatever
Solution:
B – V is proportional to T, if T halves, so will V.
7. A test tube contains 5,0 cm3 helium and is sealed with a moveable wax head. This volume
was recorded at sea level when the surrounding temperature was 293 K and the pressure
was 100 kPa. A student, keen to study the effect of altitude, carefully drives inland where
the pressure is 85 kPa, but the temperature was still 293 K.
a. Helium is said to display near ideal gas properties. Give two reasons for this.
b. Calculate the volume of the gas in the test tube inland.
Solution:
a. The volume of the He atoms (molecules) is extremely small; the force of attraction
between the atoms is extremely small.
b. P1 V1 = P2 V2
V2 =
^100h^5, 0h
85
= 5,88 cm3
8. A particular gas cylinder will explode if the pressure exceeds 14 x 103 kPa. The cylinder
has a capacity of 20 dm3 and it contains 100 mol of a propane and butane mixture. Using
appropriate gas law equations, calculate the maximum temperature that the cylinder can
be exposed to.
Solution:
PV = nRT
PV
T = nR
Note that everything must be in SI units. Here we have used Pa for pressure and m3 for
volume. Consider making this a rule for this equation for learners, to prevent incorrect
mixing of units.
Tmax =
14×106 ×20×10 -3
100×8, 31
Tmax = 337K
64
Grade 11 PHYSICAL SCIENCES Term 2
TOPICTOPIC:
7: Ideal
Gases and
Thermal
properties
Whatever
LESSON:
whatever
CHALLENGE LEVEL QUESTIONS
a. Now that learners have mastered the basic calculations, they are ready to deal with
more challenging questions.
b. These questions require learners to manipulate the equation to change the subject of
the formula.
How to tackle these questions in the classroom:
•
Work through these examples with learners.
•
Tell learners that this is a more challenging version of what they have been doing.
•
Write the first example on the chalkboard.
•
Ask learners to look at the example and see if they can work out what must be done /
what is different.
•
Discuss learners’ ideas, and ask probing questions to extend their answers.
•
Try to be positive in these interactions, to encourage critical thinking and questioning.
•
Ensure that learners copy down both the question and the solution into their workbooks.
Key Teaching:
a. In these more challenging examples, learners must manipulate the data and/or change
the subject of the formula. They also need to convert to the correct units in certain
examples.
b. Learners must convert units if needed. Often it is easier to substitute the values into the
equation first before rearranging the equation.
c. Once learners have done this, they should then change the subject of the formula.
d. Learners must be able represent the relationships graphically.
Grade 11 PHYSICAL SCIENCES Term 2
65
TOPICTOPIC:
7: Ideal
Gases and
Thermal
properties
Whatever
LESSON:
whatever
9. Assume that oxygen is an ideal gas and complete the following sketch graph of PV against
T for various values of temperature and pressure.
PV
T(K)
This particular sample of gas has a volume of 3,60 dm3 at STP.
a. Calculate the value that the slope of the graph should have.
b. At very high pressures, it is found that the PV values for oxygen no longer agree with
those expected for an ideal gas. Assuming that no condensation has taken place, how
would those PV values deviate?
c. Mention one factor to which the deviation, given above, can be attributed.
d. When the temperature of a sample of oxygen gas in a 200 cm3 container is 27 °C, the
pressure is 149,58 kPa.
i.
Calculate the number of moles of gas present.
ii. Thus, show that oxygen gas is diatomic, if 0,348 g of gas is present.
Solution:
a. Sketch graph of PV against T
PV
T(K)
The value that the slope of the graph should have:
PV = nRT
y=mx
so the slope is nR
n = V/V0
66
Grade 11 PHYSICAL SCIENCES Term 2
TOPICTOPIC:
7: Ideal
Gases and
Thermal
properties
Whatever
LESSON:
whatever
= 3,6/22,4
= 0,16 mol
nR = 0,16 x 8,314
= 1,34 JK-1
b. At very high pressures, PV values are greater than expected.
c. The real size of the molecules.
d. T = 300 K; V = 0,2 dm3= 0,2x10-3 m3;
i.
p = 149,58 x 103 Pa
the number of moles of gas present
PV = nRT
3
PV ^149 580h^0, 2x10 h
n = RT =
^8, 31h^300h
= 0,12 mol
ii. oxygen gas is diatomic
M= m/n = 0,384/0,12 = 32 g.mol-1
Therefore oxygen is diatomic as each atom has a molar atomic mass of 16 g.mol-1
and 2 x 16 =32.
10. a.
What does n represent in the equation PV = nRT?
b. Two vessels A and connected by a thin tube and a valve as shown in the sketch. A has
a volume V1 while B has a volume of V2. A contains air at a pressure of P1 and B has air
at a pressure of P2.
A
B
P1
P2
V1
V2
T
T
n1
n2
The valve is now opened. If the temperature T of the air in the vessel remains constant
throughout the experiment, derive the formula for the final pressure P in the vessels.
Hint n1 + n2 remains constant. c.
What is the relationship between the average kinetic energy of the molecules in a gas
and its kelvin temperature? Grade 11 PHYSICAL SCIENCES Term 2
67
Whatever
LESSON:
whatever
TOPICTOPIC:
7: Ideal
Gases and
Thermal
properties
d. The mass of a helium atom is 4u and that of a methane molecule is 16u. If both gases
are at the same temperature, calculate the ratio of the average velocities of their
molecules i.e.
average velocity of helium atom
.
average velocity of methane molecule
Solution:
a. n stands for the number of molecules in the equation PV = nRT.
b. Hint n1 + n2 remains constant.
P1 V1
P2 V2
n1 = RT
n2 = RT
therefore n1 + n2 =
Pfinal =
P1 V1 + P2 V2
RT
n final RT
Vfinal
=
+ P2 V2 k
a P1 V1RT
RT
=
P1 V1 + P2 V2
V1 + V2
V1 + V2
c. Kelvin temperature is a measure of the average kinetic energy of the molecules and
the kelvin temperature is directly proportional to the average kinetic energy of the
molecules.
d. Since they are at the same temperature average kinetic energy of helium atom=
average kinetic energy of methane molecule.
1
2
2 mv helium atom = 1
1
2
2 mv methane molecule
1
2
2 4uv helium atom = 1
1
2
2 16uv methane molecule
1v2helium atom
=1
4v2methane molecule
2
helium atom
2
methane molecule
v
v
=4
average velocity of helium atom
=2
average velocity of methane molecule
68
Grade 11 PHYSICAL SCIENCES Term 2
Whatever
LESSON:
whatever
TOPICTOPIC:
7: Ideal
Gases and
Thermal
properties
CHECKPOINT
At this point in the topic, learners should have mastered:
1. The calculation involving Boyle’s law, Charles’ law, Gay Lussac’s law and the general
gas equation.
2. The manipulation of the equation to calculate one of the other variables in the
equation.
Check learners’ understanding of these concepts by getting them to work through:
WORKSHEET PACK: IDEAL GASES AND THERMAL PROPERTIES WORKSHEET: QUESTIONS 4-6
•
Check learners’ understanding by marking their work with reference to the
memorandum.
•
If you cannot photocopy the memorandum for each learner, make three or four copies
of it and place these on the walls of your classroom.
3.
•
Allow learners time to mark their own work.
•
Encourage the learners to learn from the mistakes they make.
TEMPERATURE AND HEATING, PRESSURE
INTRODUCTION
This section reinforces the idea of temperature and pressure in terms of the movement of the
particles. So doubling temperature doubles the average kinetic energy of the particles, and the
average speed of the particles increases by
2.
For an explanation of pressure, see the Concept Explanation and Clarification in Motion of
particles: Kinetic theory of gases.
Grade 11 PHYSICAL SCIENCES Term 2
69
TOPICTOPIC:
7: Ideal
Gases and
Thermal
properties
Whatever
LESSON:
whatever
INTRODUCTORY LEVEL QUESTIONS
a. The basic questions are to ensure that the learners understand the concept how
temperature and pressure are related to the behaviour of the particles.
b. There are the calculations based on work already covered, leading into explanations.
How to tackle these questions in the classroom:
•
Work through these examples with learners.
•
Explain each step of the calculation to the learners as you complete it on the chalkboard.
•
Learners must copy the question as well as the solution into their workbook.
11. The volume of a particular tyre is 9,0 dm3. Two thirds of the contents of the tyre is nitrogen
gas and one third is oxygen gas.
a. Which gas exerts a greater pressure in the tyre? Explain your answer.
b. The tyre is driven for 100 km at high speed and the temperature of the tyre increases.
Explain why the tyre (which is slightly elastic) looks more rigid immediately after the
journey than before.
Solution:
a. Nitrogen exerts a greater pressure because there is more nitrogen gas than oxygen gas
(n α T).
b. As temperature increases, so does pressure in a fixed volume environment. This makes
the tyre more rigid.
12. At the same temperature, the molecules of all gases have the same:
A
average kinetic energy
B
average velocity
C
average mass
D
volume
Solution:
A – from the concept of temperature.
70
Grade 11 PHYSICAL SCIENCES Term 2
TOPICTOPIC:
7: Ideal
Gases and
Thermal
properties
Whatever
LESSON:
whatever
CHALLENGE LEVEL QUESTIONS
a. Now that learners have mastered the basic calculations, they are ready to deal with more
challenging questions.
b. These questions require learners to manipulate the equation to change the subject of
the formula.
How to tackle these questions in the classroom:
•
Work through these examples with learners.
•
Tell learners that this is a more challenging version of what they have been doing.
•
Write the first example on the chalkboard.
•
Ask learners to look at the example and see if they can work out what must be done /
what is different.
•
Discuss learners’ ideas, and ask probing questions to extend their answers.
•
Try to be positive in these interactions, to encourage critical thinking and questioning.
•
Ensure that learners copy down both the question and the solution into their workbooks.
Key Teaching:
In these more challenging examples, learners must manipulate the data and/or change the
subject of the formula.
13. The sketch below is of a gas syringe. The plunger is free to move. A sample of nitrogen,
initially at room temperature is trapped in the syringe at atmospheric pressure, then the end
of the syringe is slowly immersed in hot water at 77 ˚C.
120 cm 3
a. Explain why the pressure in the syringe remains at atmospheric pressure, even when
the end of the syringe is immersed in hot water.
Grade 11 PHYSICAL SCIENCES Term 2
71
TOPICTOPIC:
7: Ideal
Gases and
Thermal
properties
Whatever
LESSON:
whatever
b. Explain, in terms of the kinetic model of matter, why the volume of the gas increases.
Solution:
a. Because the plunger can move, it will adjust so that the forces from inside and outside
are equal i.e. the pressures will be equal.
b. As temperature increases, the average kinetic energy of the particles increases. This
means that they collide with the walls of the container more frequently and with greater
force. This would lead to a greater pressure, but the container can expand, so it does so
to enlarge the container to reduce the frequency of the collisions per unit surface area,
until the pressures inside and outside are equal.
CHECKPOINT
At this point in the topic, learners should have mastered:
1. The calculations involving all the gas laws.
2. The manipulation of the equation to calculate one of the other variables in the
equation
3. The conversion of units when needed.
As this section revises concepts already covered, there are no further worksheet
questions.
CONSOLIDATION
•
Learners can consolidate their learning by completing; Worksheet Pack: Ideal Gases and
Thermal Properties: Consolidation Exercise.
•
Photocopy the exercise sheet for the learners. If that is not possible, learners will need to
copy the questions from the board before attempting to answer them.
•
The consolidation worksheet should be marked by the teacher so that she/he is aware of
each learner’s progress in this topic.
•
Please remember that further consolidation should also be done by completing the
examples available in the textbook.
•
It is important to note that this consolidation exercise is NOT scaffolded.
•
It should not be administered as a test, as the level of the work may be too high in
its entirety.
72
Grade 11 PHYSICAL SCIENCES Term 2
TOPICTOPIC:
7: Ideal
Gases and
Thermal
properties
Whatever
LESSON:
whatever
ADDITIONAL VIEWING / READING
In addition, further viewing or reading on this topic is available through the following web links:
1. https://www.youtube.com/watch?v=whic90TMgIs
Video of Boyle’s law experiment, with data to plot (about 5 min 50 s).
2. https://www.youtube.com/watch?v=HrdQ7kJWQfc
An animation to show how temperature affects pressure (about 30 s).
3. https://www.youtube.com/watch?v=pfxSw9SbX9o
Video talking about temperature scales (2 min 55 s.)
4. https://phet.colorado.edu/en/simulation/legacy/gas-properties
A simulation where you can change gas conditions, it shows the particles, but needs Java
to be loaded.
Grade 11 PHYSICAL SCIENCES Term 2
73
TOPIC 8:TOPIC:
Quantitative
Whatever
aspects
LESSON:
of Chemical
whateverChange
A
INTRODUCTION
•
This topic runs for 12 hours.
•
For guidance on how to break down this topic into lessons, please consult the NECT
Planner & Tracker.
•
Quantitative aspects of Chemical Change (also called stoichiometry) forms part of the
content area Chemical Change.
•
Chemical Change counts as 47% in the final chemistry exam.
•
Quantitative Chemistry counts approximately 20% to 25 % of the final Chemistry
examination.
•
This section will be built into many topics in grade 12, and may be examined in Organic
chemistry and rates of reactions; it is vital in Chemical equilibrium, especially in the
equilibrium constant calculations; it will be examined in the Acids and bases section, and
may be asked in the electrochemical section. Further, some aspects of this were dealt
with in the previous topic, Ideal gases.
CLASSROOM REQUIREMENTS FOR THE TEACHER
•
Chalkboard.
•
Chalk.
•
Grade 11 Chemistry Examination Data Sheet.
CLASSROOM REQUIREMENTS FOR THE LEARNER
74
•
A4, 3 Quire exercise book, for notes and exercises.
•
Scientific calculator is essential – Sharp or Casio calculators are highly recommended.
•
Pen.
Grade 11 PHYSICAL SCIENCES Term 2
TOPIC 8:TOPIC:
Quantitative
Whatever
aspects
LESSON:
of Chemical
whateverChange
B
SEQUENTIAL TABLE
PRIOR KNOWLEDGE
CURRENT
Grade 10
Grade 11
• Stoichiometry
• Stoichiometry
• The mole concept
• Molar volume of gases.
• Molecular and formula
• Concentration
masses
• Limiting reagents
• Determining the
• Volume relationships
composition of
in gaseous reactions.
substances
• Amount of substance
(mole), molar volume
• Previously in gr 11 in
Ideal gases
of gases, concentration
LOOKING FORWARD
Grade 12
• These quantitative
concepts will be examined
in:
• Acids and bases
• Equilibrium
• They may be examined in:
• Electrochemical
reactions,
• Organic chemistry
• Reaction rates or
of solutions
• Any other section
Grade 11 PHYSICAL SCIENCES Term 2
75
TOPIC 8:TOPIC:
Quantitative
aspects
of Chemical
Whatever
LESSON:
whateverChange
C
GLOSSARY OF TERMS
Please note: The highlighted definitions and laws are ones that learners must be able to
state and are given in the CAPS document. For examination purposes, learners must know
these definitions and laws by heart, and must write them exactly as they appear here.
TERM
DEFINITION
Molar volume of a gas
The volume of 1 mole of a gas at STP ( 22, 4dm 3 )
STP
Standard temperature and pressure
(0cC; 1atm pressure i.e.101, 3kPa)
Relative molecular mass/
The sum of the masses in a molecule or formula unit
formula mass
The mole
The amount of substance that has the same number of particles
as there are atoms in 12 g of C-12
Avogadro’s number
6, 02×1023
Molar mass
The mass of 1 mole of a substance
Concentration
The number of moles of solute in a given volume of solvent
Standard solution
A (stable) solution of known concentration
Empirical formula
The simplest whole number ratio of the elements making up
a compound
Molecular formula
The actual number of atoms making up a molecule
Limiting reagent
The reactant that will be used up totally in a chemical reaction
Theoretical yield
The amount of product that is expected from a reaction
Percentage yield
The ratio of the actual yield to the theoretical yield, expressed
as a percentage.
76
Grade 11 PHYSICAL SCIENCES Term 2
TOPIC 8:TOPIC:
Quantitative
aspects
of Chemical
Whatever
LESSON:
whateverChange
D
ASSESSMENT OF THIS TOPIC
•
This topic will be assessed in the mid-year examinations and in all examinations going
forward. These concepts can be examined in a number of contexts (e.g. acid-base
reactions or chemical equilibrium).
Grade 11 PHYSICAL SCIENCES Term 2
77
TOPIC 8:TOPIC:
Quantitative
aspects
of Chemical
Whatever
LESSON:
whateverChange
TARGETED SUPPORT OFFERED
Please note that this booklet does not address the full topic – only targeted support related to common challenges is offered.
CAPS PAGE
NUMBER
•
SUB TOPIC
82
1. Key concepts and possible misconceptions are clarified and explained:
a. A general introduction highlighting areas of weakness experienced by the
candidates in gr 12 examinations.
b. Molar volume of gases
c. Concentration of solutions
2. Calculations and questions are modelled and practised at different levels:
a. Introduction level calculations involving the mole concept, volumes of gases at
STP and concentrations of solutions
b. Challenge level calculations involving the mole concept, volumes of gases at
STP and concentrations of solutions
For further guidance on full lesson planning, please consult CAPS, the NECT Planner & Tracker and the textbook.
Molar Volume
82
1. Key concepts and possible misconceptions are clarified and explained:
a. Empirical formulae
b. Molar volume of gases
2. Calculations and questions are modelled and practised at different levels:
a. Introduction level calculations involving the mole concept, masses, volumes of
gases at STP and concentrations of solutions from reaction equations
b. Challenge level calculations involving the mole concept, masses, volumes of
gases, and concentrations of solutions from reaction equations
calculations
in gaseous
relationships
Volume
calculations
stoichiometric
complex
More
of solutions
concentration
of gases and
83
•
TIME
ALLOCATION
3 hours
6 hours
3 hours
1. Key concepts and possible misconceptions are clarified and explained:
a. The volumes of gases produced from chemical reactions
2. Calculations and questions are modelled and practised at different levels:
a. Introduction level calculations involving the mole concept, masses, volumes of
gases at STP and concentrations of solutions from reaction equations
b. Challenge level calculations involving the mole concept, masses, volumes of
gases, and concentrations of solutions from reaction equations
Grade 11 PHYSICAL SCIENCES Term 2
78
BREAKDOWN OF TOPIC AND TARGETED SUPPORT OFFERED
E
TOPIC 8:TOPIC:
Quantitative
aspects
of Chemical
Whatever
LESSON:
whateverChange
F
TARGETED SUPPORT PER SUB TOPIC
1.
THE MOLE CONCEPT
INTRODUCTION
As mentioned earlier, this section is examined in many different sections in the grade 12
examination. So the learners have to be very familiar with the mole concept so that they can
use it in different contexts. The mole concept was introduced in grade 10, however, learners
often find it an abstract and difficult concept. Avogadro’s number, which is associated with the
mole, is too large for us to really understand (6,02 x 1023 marbles would be 116 times higher
than Mount Everest, with a base the approximately size of the USA!) The reason that the mole
is so big is because it describes atoms and molecules, which are extremely small. So the mole
is a link of the world we can see and measure (like 12 g of carbon, or 22 dm3 ( 22l ) of a gas at
STP, to the world we cannot see or measure the world of atoms and molecules.
The diagnostic reports from grade 12 for 2015 and 2016 both show that this section is an area
of weakness for many learners, even in simpler areas like the calculation of molar masses. The
correct application of ratios from reaction equations is also generally poorly handled. These
notes will focus on these types of examples.
The CAPS suggest a flow diagram for stoichiometric calculations.
Vgas
N
m
n1
PV/RT
Ratios from balanced
reaction equation
c
m
Vgas
N
n2
c
PV/RT
The word stoichiometry comes from the Greek, meaning to walk (or measure) the elements.
Usually the best way to measure the elements or compounds is by the concept of mole, which
actually defines how much of a substance there is present. A good approach to most problems
in this section is to convert whatever you are given to the number of moles; use the ratios (often
from the chemical reaction) to find the moles of the other substance and then to convert to the
desired answer.
Grade 11 PHYSICAL SCIENCES Term 2
79
Whatever
LESSON:
whateverChange
TOPIC 8:TOPIC:
Quantitative
aspects
of Chemical
CONCEPT EXPLANATION AND CLARIFICATION: MOLAR VOLUME OF GAS AND CONCENTRATION OF SOLUTIONS
From the Ideal gas laws, we can prove that 1 mole of any gas (that is behaving like an ideal
gas) will occupy 22,4 dm3 at STP. The STP values (273 K and 101,3 kPa i.e. 1 atm pressure)
are to be learnt. But most importantly, it must be stressed to the learners that the value of 22,4
only applies to a gas (at STP.) Many learners try to use this value inappropriately, for example
in concentration calculations.
V
This leads to n =
22, 4 for a gas.
CONCEPT EXPLANATION AND CLARIFICATION: GAS REACTIONS
If a there are two gases in a reaction, the ratio of their volumes will be equal to the ratio from
the balanced reaction equation. For example:
N2(g) + 2O2(g) 2NO2(g)
1 molecule of N2 reacts with 2 molecules of O2 to form 2 molecules of NO2
1 mole of N2 reacts with 2 moles of O2 to form 2 moles of NO2
and 1 dm3 of N2 reacts with 2 dm3 of O2 to form 2 dm3 of NO2.
This method can be used to solve certain calculations, or one can work out the moles in each case.
CONCEPT EXPLANATION AND CLARIFICATION: CONCENTRATION OF SOLUTIONS
The concentration of solutions is calculated in mol.dm-3. The definition for a standard solution is
also needed for this section.
INTRODUCTORY LEVEL QUESTIONS
a. These are the basic calculations that learners will be required to perform at this stage
in the topic.
b. Their purpose is to familiarise the learners with the equation in straight-forward
calculations.
How to tackle these questions in the classroom:
80
•
Work through these examples with learners.
•
Explain each step of the calculation to the learners as you complete it on the chalkboard.
•
Learners must copy the question as well as the solution into their workbook.
Grade 11 PHYSICAL SCIENCES Term 2
Whatever
LESSON:
whateverChange
TOPIC 8:TOPIC:
Quantitative
aspects
of Chemical
1. Carbon reacts with oxygen to form carbon dioxide, according to the equation:
C ^ s h + O2 (g) " CO2 (g)
5,75 dm3 of oxygen at STP reacts.
a. How many moles of oxygen has reacted?
b. How many moles of carbon dioxide will be formed?
c. What volume of carbon dioxide will be formed at STP
Solution:
V
5, 75
a. n =
22, 4 = 22, 4 = 0, 26mol
b. The reaction gives 1O2 " 1 CO2 so 0,26 mol CO2 forms.
c. V = n×22, 4 = 0, 26×22, 4 = 5, 75dm 3 OR from the reaction equation, the mole ratio is
equal to the volume ratio, so VCO2 = 5,75 dm3.
2. A standard 0,15 mol.dm-3 sodium carbonate solution is prepared in a 250 cm3 volumetric flask.
a. Give the formula for sodium carbonate
b. How many moles of sodium carbonate are needed to prepare this solution?
c. What mass of sodium carbonate is needed to prepare this solution?
Solution:
a. Na2CO3
b. n = cV = 0, 15×0, 25 note the conversion of cm3 to dm3
= 0, 0375mol
c.
m = nM = 0, 0375× ^23×2 + 12 + 16×3h
=3,975 g
Grade 11 PHYSICAL SCIENCES Term 2
81
TOPIC 8:TOPIC:
Quantitative
Whatever
aspects
LESSON:
of Chemical
whateverChange
CHALLENGE LEVEL QUESTIONS
a. Now that learners have mastered the basic calculations, they are ready to deal with more
challenging questions.
b. These questions require learners to manipulate the equation to change the subject of
the formula.
How to tackle these questions in the classroom:
•
Work through these examples with learners.
•
Tell learners that this is a more challenging version of what they have been doing.
•
Write the first example on the chalkboard.
•
Ask learners to look at the example and see if they can work out what must be done /
what is different.
•
Discuss learners’ ideas, and ask probing questions to extend their answers.
•
Try to be positive in these interactions, to encourage critical thinking and questioning.
•
Ensure that learners copy down both the question and the solution into their workbook.
Key Teaching:
a. In these more challenging examples, learners must manipulate the data and/or change
the subject of the formula, to solve for mass or number of moles.
b. Learners must work step by step, often it is easier to substitute the values into the
equation first.
3. 64 g of oxygen gas reacts with sulfur, according to the following equation:
S(s) + O2(g) " SO2(g)
What volume of SO2 gas (at STP) will be produced by this reaction?
82
A
44,8 dm3
B
1,2 dm3
C
2 dm3
D
64 dm3
Grade 11 PHYSICAL SCIENCES Term 2
TOPIC 8:TOPIC:
Quantitative
Whatever
aspects
LESSON:
of Chemical
whateverChange
Solution:
A
2 mol (
64
32, 1 ) O2 react, so 2 mol SO2 forms.
4. Hydrogen and oxygen react according to the equation: 2H 2 (g) + O2 (g) " 2H 2O (g)
a. What volume of oxygen will react with 4,0 dm3 of hydrogen at STP?
a. What volume of water vapour will be produced?
Solution:
4
V
a. The ratio is 1:2 or 2:4, so 2,0 dm3 O2 will react OR nO =
22, 4 = 22, 4 = 0, 179mol
2
The ratio is 1:2 so nCO2 = 0, 089mol
V = n×22, 4 = 0, 089×22, 4 = 2, 0dm3
b. The ratio is 2:2 or 4:4; so 4,0 dm3 H2O will be formed OR nO = 0, 179mol
2
The ratio is 2:2 so n = 0, 179mol
V = n×22, 4 = 0, 179×22, 4 = 4, 0dm3
5. A standard solution of Mg(OH)2 is made up so that it will have a volume of 0,25 dm3 and a
concentration of 0,5 mol.dm-3. The standard solution is made up using distilled water.
a. Name the solute used to make this solution.
b. Calculate the mass of solid Mg(OH)2 required to make up the standard solution.
Solution:
a. magnesium hydroxide
b. n = cV = 0, 5×0, 25 (both subs) = 0, 125mol
m = nM = 0, 125×58, 3 = 7, 29g
Grade 11 PHYSICAL SCIENCES Term 2
83
TOPIC 8: Quantitative
aspects
of Chemical
Change
TOPIC: Whatever
LESSON:
whatever
CHECKPOINT
At this point in the topic, learners should have mastered:
1. The calculation number of moles from volumes of gases.
2. The calculation number of moles from masses of substances.
3. The use of ratios from reaction equations.
4. The calculations of concentrations of solutions..
Check learners’ understanding of these concepts by getting them to work through:
WORKSHEET PACK: QUANTITATIVE ASPECTS OF CHEMICAL CHANGE WORKSHEET: QUESTIONS 1-4
•
Check learners’ understanding by marking their work with reference to the
memorandum.
•
If you cannot photocopy the memorandum for each learner, make three or four copies
of it and place these on the walls of your classroom.
2.
•
Allow learners time to mark their own work.
•
Encourage the learners to learn from the mistakes they make.
STOICHIOMETRIC CALCULATIONS
CONCEPT EXPLANATION AND CLARIFICATION: STOICHIOMETRIC CALCULATIONS
Many learners find these challenging, but they can be fun. Try to link as many as possible to
practical activities, by doing titrations and the recommended practical of getting PbO2 from
Pb(NO3)2.
CONCEPT EXPLANATION AND CLARIFICATION: EMPIRICAL FORMULA
This was covered in grade 10, but many learners find these calculations challenging. If no mass
of the substance is given, then learners must treat the sample as if they were given 100 g of
the sample, and then work out the moles of each type of element. They must work out the ratio
of the elements, beginning by dividing each number of moles by the smallest number. This will
give the ratio of the elements in the sample, which is called the empirical (from experiment)
formula. It is called this because some chemical analysis experiments give these ratios, from
which the empirical formula can be calculated.
84
Grade 11 PHYSICAL SCIENCES Term 2
TOPIC 8:TOPIC:
Quantitative
Whatever
aspects
LESSON:
of Chemical
whateverChange
INTRODUCTORY LEVEL QUESTIONS
a. These are the basic calculations that learners will be required to perform at this stage in
the topic.
b. Their purpose is to familiarise the learners with the equation and to use stoichiometric
ratios in increasingly unusual or complex contexts.
How to tackle these questions in the classroom:
•
Work through these examples with learners.
•
Explain each step of the calculation to the learners as you complete it on the chalkboard.
•
Learners must copy the question as well as the solution into their workbook.
6. a. Define the term molar mass of a substance.
b. Calculate the number of moles of water in 100 g of water.
Solution:
a. The mass of 1 mole of a substance
m
100
= 5, 56mol
b. n = M =
^16 + 2h
7. Methyl benzoate is a compound used in the manufacture of perfumes. It is found that a
5,325 g sample of methyl benzoate contains 3,758 g of carbon, 0,316 g of hydrogen and
1,251 g of oxygen.
a. Define the term empirical formula.
b. Determine the empirical formula of methyl benzoate.
c. If the molar mass of methyl benzoate is 136 g⋅mol-1, what is its molecular formula?
Solution:
a. The simplest whole number ratio of the elements making up a compound.
0, 316
3, 758
1, 251
=
; nH = 1 = 0, 316mol ; nO =
0
,
3131
mol
12
16 = 0, 0, 078mol
0, 3131 0, 316 0, 0, 078
nC: nH: nO = 0, 078 : 0, 078 : 0, 078 = 4: 4: 1
b. nC =
So, the empirical formula is C4H4O
c.
1
MC H O = 68g.mol -1 = 2 ^136h So molecular formula is C8H8O2
4
4
Grade 11 PHYSICAL SCIENCES Term 2
85
TOPIC 8: Quantitative
aspects
of Chemical
Change
TOPIC: Whatever
LESSON:
whatever
8. A sample of sodium carbonate was reacted with dilute hydrochloric acid in a closed
container according to the following equation:
Na2CO3 (s) + 2HCl (aq) → 2NaCl (aq) + CO2 (g) + H2O (l)
The carbon dioxide gas produced was collected at STP and occupied a volume of
0,336 dm3.
a. Calculate the number of moles of carbon dioxide produced.
b. Calculate the number of carbon dioxide molecules in the sample collected.
c. Calculate the mass of sodium chloride formed in this reaction.
d. If the concentration of the hydrochloric acid is 0,10 mol.dm-3 what is the minimum
volume of hydrochloric acid needed for the reaction to run to completion?
Solution:
0, 336
V
a. n =
22, 4 = 22, 4 = 0, 015mol
b.
N = n×6, 02×1023 = 0, 015×6, 02x1023 = 9, 0×1021 molecules
c.
nNaCl: nCO = 2: 1 ^ from reaction equationh
2
nNaCl = 0, 03mol
m = nM = 0, 03�^23 + 35, 45h = 1, 755g
d. nHCl: nCO = 2: 1 ^ from reaction equationh
2
nHCl = 0, 03mol
n 0, 03
V = c = 0, 1 = 0, 3dm3
9. 20 g of sodium hydroxide is completely reacted in excess sulphuric acid according to the
following balanced equation:
2NaOH + H2SO4 →
Na2SO4 +
2H2O
a. Name both of the products in this reaction.
b. Calculate how many moles of sodium hydroxide were added to the sulphuric acid.
c. What mass of Na2SO4 is produced in this reaction?
Solution:
a. Sodium sulphate; Water
86
Grade 11 PHYSICAL SCIENCES Term 2
TOPIC 8:TOPIC:
Quantitative
Whatever
aspects
LESSON:
of Chemical
whateverChange
b. 𝑀𝑁𝑎𝑂𝐻 =23 + 16 + 1 =40 𝑔.𝑚𝑜𝑙-1
m
c.
20
𝑛= M =
40 = 0,5 𝑚𝑜𝑙
NaOH
2
0,5 mol
:
:
:
Na2SO4
1
0,25 mol
MNa SO =2(23)+32,1+4(16)=142,1 𝑔.𝑚𝑜𝑙-1
2
4
𝑚 = 𝑛 × 𝑀 = 0,25 ×142,1
𝑚 = 35,5 𝑔
CHALLENGE LEVEL QUESTIONS
a. Now that learners have mastered the basic calculations, they are ready to deal with more
challenging questions.
b. These questions require learners to manipulate the equation in a more complex context.
How to tackle these questions in the classroom:
•
Work through these examples with learners.
•
Tell learners that this is a more challenging version of what they have been doing.
•
Write the first example on the chalkboard.
•
Ask learners to look at the example and see if they can work out what must be done /
what is different.
•
Discuss learners’ ideas, and ask probing questions to extend their answers.
•
Try to be positive in these interactions, to encourage critical thinking and questioning.
•
Ensure that learners copy down both the question and the solution into their workbooks.
Key Teaching:
a. In these more challenging examples, learners must manipulate the data and/or change
the subject of the formula, to solve for mass, moles, volume, concentration or percentage
yield
b. It is often easier for learners to substitute the values into the equation first
c. Once learners have done this, they should then change the subject of the formula.
Grade 11 PHYSICAL SCIENCES Term 2
87
TOPIC 8: Quantitative
aspects
of Chemical
Change
TOPIC: Whatever
LESSON:
whatever
10. 50 g of magnesium carbonate is added to 500 cm3 of hydrochloric acid with a concentration
of 0,75 mol.dm-3. The equation for the reaction is given below:
MgCO3 + 2HCl
→
MgCl2 + CO2 + H2O
The carbon dioxide gas is collected at STP.
a. What are the standard conditions used when conducting an experiment at STP?
b. Determine which reactant is the limiting reactant
c. If the percentage yield of the experiment is 85%, calculate the volume of carbon dioxide
collected at the end of the experiment at STP.
Solution:
a. Temperature of 0°C; Pressure of 101.3 kPa
b.
MMgCO =24,3 + 12 + 3 x 16 = 84,3 𝑔.𝑚𝑜𝑙-1
3
nMgCO = 𝑚/𝑀
3
nMgCO =50/84.3
3
nMgCO = 0,593 𝑚𝑜𝑙
3
MHCl = 1 + 35,45 = 36,45 𝑔.𝑚𝑜𝑙—1
nHCl = c × V
nHCl = 0,75 × 0,5
nHCl = 0,375 𝑚𝑜𝑙
0,593 mol MgCO3 would require 1,186 mol HCl in order to completely react. MgCO3 is in
excess. HCl is the limiting reagent.
c.
nHCl = 0,375; so nCO = 0,1875
2
VCO = n×22, 4 = 4, 2dm3
2
But only 85% yield, so V = 4, 2×85 = 3, 57dm 3
88
Grade 11 PHYSICAL SCIENCES Term 2
TOPIC 8:TOPIC:
Quantitative
Whatever
aspects
LESSON:
of Chemical
whateverChange
11. Chlorine gas can be produced by heating calcium hypochlorite, Ca(OCl)2, in dilute
hydrochloric acid.
Ca(OCl)2(s) + 2HCl(aq) → Ca(OH)2(aq) + 2Cl2(g)
a. Calculate the mass of calcium hypochlorite that would be needed to produce 0,096
litres of chlorine gas at STP.
b. If the calcium hypochlorite used was only 76% pure, what was the mass of the original
sample?
c. What assumption do you have to make in (b) in order to determine the mass of the
original sample from the given information?
Solution:
a. nChlorine =
0, 096
V
22, 4 = 22, 4 = 0,00428 mol
nCalcium hypochlorite : nChlorine = 1 : 2
nCalcium hypochlorite = 0,5(0,00428) = 0,00214 mol
mCalcium hypochlorite = nM = (0,00214)(143) = 0,306 g
b. moriginal = 0,306/0,76 =0,402 g
c. None of the contaminants of the original sample can produce chlorine or any other kind
of gas in the above reaction. They have to be totally unreactive to hydrochloric acid.
12. An unknown mass, x g, of solid sodium hydroxide reacts with 22,18 cm3 of 0,15 mol.dm-3
sulphuric acid according to the equation:
2NaOH ^ s h + H2 SO4 ^aqh " Na2 SO4 ^aqh + 2H2 O (l)
a. How many moles of sulphuric acid are used in this reaction?
b. How many moles of sodium hydroxide are needed to react completely with the acid?
c. Calculate the mass of sodium hydroxide that reacted.
Solution:
a. na = ca Va = 0, 15×0, 02218 = 0, 0033mol
b. nb = 2×0, 0033 = 0, 0066mol
Use ratios (COE from a)
c.
(COE from b)
m = n.M = 0, 0066×40 = 0, 26g
Grade 11 PHYSICAL SCIENCES Term 2
89
TOPIC 8: Quantitative
aspects
of Chemical
Change
TOPIC: Whatever
LESSON:
whatever
CHECKPOINT
At this point in the topic, learners should have mastered:
1. The calculation of mass, moles, volume, concentration or percentage yield.
2. The manipulation of the reaction equation to calculate ratios of moles of various
substances.
3.
VOLUME RELATIONSHIPS IN GASEOUS REACTIONS
Concept Explanation and Clarification:
It is remarkable how much more volume a gas takes up than a solid or a gas. 18 g of water
goes from about 18 cm3 (3 12 teaspoons) to 22 dm3 when going from liquid to gas at STP. It is
worthwhile displaying a teaspoon and 22 1l coke bottles to your learners so demonstrate this
expansion.
This rapid expansion is used in airbags, where sodium azide reacts to form nitrogen gas (the
sodium that forms is further reacted away into a stable compound), according to the equation:
2NaN3(s)  2Na(s) + 3 N2(g). This principle is also used in explosive where the rapid formation
of a heated gas is used, for example in mining.
INTRODUCTORY LEVEL QUESTIONS
a. These are the basic calculations that learners will be required to perform at this stage
in the topic.
b. Their purpose is to familiarise the learners with the equation, but not to change the
subject of the formula.
How to tackle these questions in the classroom:
90
•
Work through these examples with learners.
•
Explain each step of the calculation to the learners as you complete it on the chalkboard.
•
Learners must copy the question as well as the solution into their workbook.
Grade 11 PHYSICAL SCIENCES Term 2
TOPIC 8:TOPIC:
Quantitative
Whatever
aspects
LESSON:
of Chemical
whateverChange
13. Ammonium nitrate is the basis of an explosive used in mines. It can decompose according
the to the following equation:
2NH4NO3(s)  2N2 + 4H2O + O2
All the products are gases.
a. Calculate how many moles of ammonium nitrate is found in 100 g of the solid.
b. Find the number of moles that will be formed of:
i.
Nitrogen
ii. Water
iii. Oxygen
c. Thus, calculate the total volume of gas formed at STP
d. Calculate the total volume of gas formed at 273°C. (Hint: volume is directly proportional
to temperature.)
Solution:
m
100
= 1, 25mol
a. n = M =
^14 + 4 + 14 + 48h
b. i.
N2: 1,25 mol
ii.
H2O: 2,5 mol
iii. O2: 0,625 mol
c.
ntotal = 4, 375; V = n×22, 4 = 8dm 3
d. 273cC = 546K; 0cC = 273K; thus the temperature doubled. Thus, the volume will
double to 16 dm3.
Grade 11 PHYSICAL SCIENCES Term 2
91
TOPIC 8: Quantitative
aspects
of Chemical
Change
TOPIC: Whatever
LESSON:
whatever
CHALLENGE LEVEL QUESTIONS
a. Now that learners have mastered the basic calculations, they are ready to deal with more
challenging questions.
b. These questions require learners to manipulate the equation to change the subject of
the formula.
How to tackle these questions in the classroom:
•
Work through these examples with learners.
•
Tell learners that this is a more challenging version of what they have been doing.
•
Write the first example on the chalkboard.
•
Ask learners to look at the example and see if they can work out what must be done /
what is different.
•
Discuss learners’ ideas, and ask probing questions to extend their answers.
•
Try to be positive in these interactions, to encourage critical thinking and questioning.
•
Ensure that learners copy down both the question and the solution into their workbooks.
Key Teaching:
a. In these more challenging examples, learners must manipulate the data and/or change
the subject of the formula, to solve for mass, moles, volume, concentration or percentage
yield
b. Learners must appreciate the substantial increase in volume when solids or liquids react
to form gases.
14. A common party trick is to fill balloons with carbon dioxide. Vinegar is poured into a small
plastic bottle and the baking soda is placed into the balloon. The mouth of the balloon
is then stretched over the bottle opening and the baking soda is allowed to fall into the
vinegar, starting the reaction. One of the products, carbon dioxide gas, fills up the balloon,
hence blowing it up.
The balanced chemical reaction that occurs when vinegar and baking soda react is as
follows:
CH3COOH (aq) + NaHCO3 (s)  CH3COONa (aq) + CO2 (g) + H2O (ℓ)
92
Grade 11 PHYSICAL SCIENCES Term 2
TOPIC 8:TOPIC:
Quantitative
Whatever
aspects
LESSON:
of Chemical
whateverChange
a. “Baking soda” is the common name for NaHCO3. Give its full chemical name.
b. One teaspoon of baking soda is equivalent to 4 g of NaHCO3. Calculate the number
of moles of NaHCO3 in one teaspoon of baking soda (give your answer to 4 decimal
places).
c. 0,0377 mol of ethanoic acid (CH3COOH) is poured into the balloon when 45 cm3 of
vinegar is added. Calculate the concentration of ethanoic acid in this sample of vinegar.
Show that if the reaction proceeds as per the quantities given, NaHCO3 is in excess.
d. Assuming that the carbon dioxide gas is the only gas responsible for the filling of the
balloon, calculate the expected volume in cm3 of the balloon at room temperature once
the reaction has reached completion. (Note: Vm = 22,4 dm3.mol-1 at room temperature.)
The actual volume of the balloon that was blown up was determined to be 750 cm3.
e. Calculate the percentage yield of the carbon dioxide gas produced in this reaction.
f.
Some learners thought that these balloons would float in the same way that helium filled
balloons do. Using your knowledge of molar masses, and the equation PV=nRT, predict
if the balloons filled with carbon dioxide will float.
Solution:
a. sodium hydrogen carbonate (or sodium bicarbonate, not sodium bicarb)
m
b. n(NaHCO3) = M
4
84
=
= 0,0476 mol
c.
n
cCH3COOH = V
0, 0377
3 ^0, 015h
=
= 0,84 mol.dm-3
n(CH3COOH)
1
:
n(NaHCO3)
: 1
0,0377 : 0,0377 mol NaHCO3 required if CH3COOH reacts completely,
but 0,0476 mol is available, therefore NaHCO3 in excess
Grade 11 PHYSICAL SCIENCES Term 2
93
TOPIC 8: Quantitative
aspects
of Chemical
Change
TOPIC: Whatever
LESSON:
whatever
d. n(CH3COOH) : n(CO2)
1
: 1
` n(CO2)
= 0,0377 mol
V(CO2)theor
= nVm
need the ratio
= 0,0377 x 22,4
= 0,8444 dm3
= 844,48 cm3
e. % yield CO2
actual V
×100
theoretical V
750
=
(Fine to convert to other quantities, but units
844, 47 ×100
=
f.
must cancel)
= 88,81 %
No, balloons filled with CO2 won’t float as CO2 is more dense than air. This is because
the volume of the balloon depends on the number of moles, the pressure and the
temperature. (from PV = nRT.) But the same number of moles of CO2 (M = 44 g.mol-1)
will be much heavier than that of Helium (M = 2 g.mol-1)
94
Grade 11 PHYSICAL SCIENCES Term 2
TOPIC 8:TOPIC:
Quantitative
Whatever
aspects
LESSON:
of Chemical
whateverChange
CHECKPOINT
At this point in the topic, learners should have mastered:
1. The calculation of mass, moles, volume, concentration and percentage yield
2. The manipulation of the reaction equation to calculate ratios of moles of various
substances
3. The change in volume in reactions which produce gaseous products
Check learners’ understanding of these concepts by getting them to work through:
WORKSHEET PACK: QUANTITATIVE ASPECTS OF CHEMICAL CHANGE WORKSHEET: QUESTIONS 5-8
•
Check learners’ understanding by marking their work with reference to the
memorandum.
•
If you cannot photocopy the memorandum for each learner, make three or four
copies of it and place these on the walls of your classroom.
•
Allow learners time to mark their own work.
•
Encourage the learners to learn from the mistakes they make.
CONSOLIDATION
•
Learners can consolidate their learning by completing; Worksheet Pack: Quantitative
aspects of chemical change: Consolidation Exercise.
•
Photocopy the exercise sheet for the learners. If that is not possible, learners will need to
copy the questions from the board before attempting to answer them.
•
The consolidation worksheet should be marked by the teacher so that she/he is aware of
each learner’s progress in this topic.
•
Please remember that further consolidation should also be done by completing the
examples available in the textbook.
•
It is important to note that this consolidation exercise is NOT scaffolded.
•
It should not be administered as a test, as the level of the work may be too high to
in its entirety.
Grade 11 PHYSICAL SCIENCES Term 2
95
TOPIC 8: Quantitative
aspects
of Chemical
Change
TOPIC: Whatever
LESSON:
whatever
ADDITIONAL VIEWING / READING
In addition, further viewing or reading on this topic is available through the following web links:
1. https://chem.libretexts.org/Core/Inorganic_Chemistry/Chemical_Reactions/Stoichiometry_
and_Balancing_Reactions
Has a useful, slightly different approach to stoichiometry.
2. https://www.youtube.com/watch?v=UL1jmJaUkaQ
An unusual and fun video-clip, which deals with an introduction to stoichiometry. This is
useful to watch, although long at 12:46. Some aspects are not very relevant to what is
covered in this section, but is useful revision. It is best to watch just the 1st few minutes, as
some the later methods are not standard in CAPS.
3. https://www.youtube.com/watch?v=XnfATaoubzA
Also long, and not as exciting to watch (15:45) but a thorough approach, with a slightly
different algebraic method.
96
Grade 11 PHYSICAL SCIENCES Term 2